def test_FinFXMktVolSurface5(verboseCalibration):
###########################################################################
# Here I remove the 10D Vols
###########################################################################
if 1 == 1:
# Example from Book extract by Iain Clark using Tables 3.3 and 3.4
# print("EURUSD EXAMPLE CLARK")
valuation_date = Date(10, 4, 2020)
forName = "EUR"
domName = "USD"
forCCRate = 0.03460 # EUR
domCCRate = 0.02940 # USD
domDiscountCurve = DiscountCurveFlat(valuation_date, domCCRate)
forDiscountCurve = DiscountCurveFlat(valuation_date, forCCRate)
currencyPair = forName + domName
spotFXRate = 1.3465
tenors = ['1M', '2M', '3M', '6M', '1Y', '2Y']
atmVols = [21.00, 21.00, 20.750, 19.400, 18.250, 17.677]
marketStrangle25DeltaVols = [0.65, 0.75, 0.85, 0.90, 0.95, 0.85]
riskReversal25DeltaVols = [-0.20, -0.25, -0.30, -0.50, -0.60, -0.562]
marketStrangle10DeltaVols = [2.433, 2.83, 3.228, 3.485, 3.806, 3.208]
riskReversal10DeltaVols = [-1.258, -1.297, -1.332, -1.408, -1.359, -1.208]
marketStrangle10DeltaVols = None
riskReversal10DeltaVols = None
notionalCurrency = forName
atmMethod = FinFXATMMethod.FWD_DELTA_NEUTRAL
deltaMethod = FinFXDeltaMethod.SPOT_DELTA
volFunctionType = FinVolFunctionTypes.CLARK
alpha = 0.50 # FIT WINGS AT 10D if ALPHA = 1.0
fxMarketPlus = FinFXVolSurfacePlus(valuation_date,
spotFXRate,
currencyPair,
notionalCurrency,
domDiscountCurve,
forDiscountCurve,
tenors,
atmVols,
marketStrangle25DeltaVols,
riskReversal25DeltaVols,
marketStrangle10DeltaVols,
riskReversal10DeltaVols,
alpha,
atmMethod,
deltaMethod,
volFunctionType)
fxMarketPlus.checkCalibration(False)
def test_FinFXVanillaOptionWystupExample1():
# Example from Book extract by Uwe Wystup with results in Table 1.2
# https://mathfinance.com/wp-content/uploads/2017/06/FXOptionsStructuredProducts2e-Extract.pdf
# Not exactly T=1.0 but close so don't exact exact agreement
# (in fact I do not get exact agreement even if I do set T=1.0)
valuation_date = Date(13, 2, 2018)
expiry_date = Date(13, 2, 2019)
# In BS the FX rate is the price in domestic of one unit of foreign
# In case of EURUSD = 1.3 the domestic currency is USD and foreign is EUR
# DOM = USD , FOR = EUR
ccy1 = "EUR"
ccy2 = "USD"
ccy1CCRate = 0.030 # EUR
ccy2CCRate = 0.025 # USD
currencyPair = ccy1 + ccy2 # Always ccy1ccy2
spotFXRate = 1.20
strikeFXRate = 1.250
volatility = 0.10
notional = 1000000.0
domDiscountCurve = DiscountCurveFlat(valuation_date, ccy2CCRate)
forDiscountCurve = DiscountCurveFlat(valuation_date, ccy1CCRate)
model = FinModelBlackScholes(volatility)
# Two examples to show that changing the notional currency and notional
# keeps the value unchanged
notional = 1000000.0
callOption = FinFXVanillaOption(expiry_date, strikeFXRate, currencyPair,
FinOptionTypes.EUROPEAN_CALL, notional,
"EUR", 2)
value = callOption.value(1.0, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
notional = 1250000.0
callOption = FinFXVanillaOption(expiry_date, strikeFXRate, currencyPair,
FinOptionTypes.EUROPEAN_CALL, notional,
"USD", 2)
value = callOption.value(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
delta = callOption.delta(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
testCases.header("value", "delta")
testCases.print(value, delta)
def test_BondOptionAmericanConvergenceONE():
# Build discount curve
settlement_date = Date(1, 12, 2019)
discount_curve = DiscountCurveFlat(settlement_date, 0.05)
# Bond details
maturity_date = Date(1, 9, 2025)
issue_date = Date(1, 9, 2016)
coupon = 0.05
freq_type = FrequencyTypes.SEMI_ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
# Option Details
expiry_date = Date(1, 12, 2020)
strikePrice = 100.0
face = 100.0
testCases.header("TIME", "N", "PUT_AMER", "PUT_EUR", "CALL_AME",
"CALL_EUR")
timeSteps = range(30, 100, 10)
for numTimeSteps in timeSteps:
sigma = 0.20
a = 0.1
start = time.time()
optionType = FinOptionTypes.AMERICAN_PUT
bondOption1 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
model1 = FinModelRatesBK(sigma, a, numTimeSteps)
v1put = bondOption1.value(settlement_date, discount_curve, model1)
optionType = FinOptionTypes.EUROPEAN_PUT
bondOption2 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
model2 = FinModelRatesBK(sigma, a, numTimeSteps)
v2put = bondOption2.value(settlement_date, discount_curve, model2)
optionType = FinOptionTypes.AMERICAN_CALL
bondOption1 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
model1 = FinModelRatesBK(sigma, a, numTimeSteps)
v1call = bondOption1.value(settlement_date, discount_curve, model1)
optionType = FinOptionTypes.EUROPEAN_CALL
bondOption2 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
model2 = FinModelRatesBK(sigma, a, numTimeSteps)
v2call = bondOption2.value(settlement_date, discount_curve, model2)
end = time.time()
period = end - start
testCases.print(period, numTimeSteps, v1put, v2put, v1call, v2call)
def testBlackModelCheck():
# Checking Andersen paper using Black's model
# Used to check swaption price below - we have Ts = 1 and Te = 4
# Expect a price around 122 cents which is what I find.
valuation_date = Date(1, 1, 2020)
libor_curve = DiscountCurveFlat(valuation_date, 0.06,
FrequencyTypes.SEMI_ANNUAL)
settlement_date = Date(1, 1, 2020)
exerciseDate = Date(1, 1, 2021)
maturity_date = Date(1, 1, 2024)
fixedCoupon = 0.06
fixedFrequencyType = FrequencyTypes.SEMI_ANNUAL
fixedDayCountType = DayCountTypes.THIRTY_E_360_ISDA
notional = 100.0
# Pricing a PAY
swaptionType = FinSwapTypes.PAY
swaption = FinIborSwaption(settlement_date, exerciseDate, maturity_date,
swaptionType, fixedCoupon, fixedFrequencyType,
fixedDayCountType, notional)
model = FinModelBlack(0.20)
v = swaption.value(valuation_date, libor_curve, model)
testCases.header("LABEL", "VALUE")
testCases.print("BLACK'S MODEL PRICE:", v * 100)
def test_FinFloatIborLeg():
effective_date = Date(28, 10, 2020)
maturity_date = Date(28, 10, 2025)
spread = 0.0
freq_type = FrequencyTypes.ANNUAL
day_count_type = DayCountTypes.THIRTY_360_BOND
notional = 10.0 * ONE_MILLION
legPayRecType = FinSwapTypes.PAY
calendar_type = CalendarTypes.TARGET
bus_day_adjust_type = BusDayAdjustTypes.FOLLOWING
date_gen_rule_type = DateGenRuleTypes.BACKWARD
payment_lag = 0
principal = 0.0
swapFloatLeg = FinFloatLeg(effective_date, maturity_date, legPayRecType,
spread, freq_type, day_count_type, notional,
principal, payment_lag, calendar_type,
bus_day_adjust_type, date_gen_rule_type)
libor_curve = DiscountCurveFlat(effective_date, 0.05)
firstFixing = 0.03
v = swapFloatLeg.value(effective_date, libor_curve, libor_curve,
firstFixing)
def test_FinFXMktVolSurface2(verboseCalibration):
#print("==============================================================")
# Example from Book extract by Iain Clark using Tables 3.3 and 3.4
# print("EURJPY EXAMPLE CLARK")
valuation_date = Date(10, 4, 2020)
forName = "EUR"
domName = "JPY"
forCCRate = 0.0294 # EUR
domCCRate = 0.0171 # USD
domDiscountCurve = DiscountCurveFlat(valuation_date, domCCRate)
forDiscountCurve = DiscountCurveFlat(valuation_date, forCCRate)
currencyPair = forName + domName
spotFXRate = 90.72
tenors = ['1M', '2M', '3M', '6M', '1Y', '2Y']
atmVols = [21.50, 20.50, 19.85, 18.00, 15.95, 14.009]
marketStrangle25DeltaVols = [0.35, 0.325, 0.300, 0.225, 0.175, 0.100]
riskReversal25DeltaVols = [-8.350, -8.650, -8.950, -9.250, -9.550, -9.500]
notionalCurrency = forName
atmMethod = FinFXATMMethod.FWD_DELTA_NEUTRAL_PREM_ADJ
deltaMethod = FinFXDeltaMethod.SPOT_DELTA_PREM_ADJ
fxMarket = FinFXVolSurface(valuation_date,
spotFXRate,
currencyPair,
notionalCurrency,
domDiscountCurve,
forDiscountCurve,
tenors,
atmVols,
marketStrangle25DeltaVols,
riskReversal25DeltaVols,
atmMethod,
deltaMethod)
fxMarket.checkCalibration(verboseCalibration)
if PLOT_GRAPHS:
fxMarket.plotVolCurves()
def test_FinFXMktVolSurface4(verboseCalibration):
# USDJPY Example from Paper by Uwe Wystup using Tables 4
# print("USDJPY EXAMPLE WYSTUP")
valuation_date = Date(20, 1, 2009)
forName = "USD"
domName = "JPY"
forCCRate = 0.003525 # USD
domCCRate = 0.0042875 # JPY
domDiscountCurve = DiscountCurveFlat(valuation_date, domCCRate)
forDiscountCurve = DiscountCurveFlat(valuation_date, forCCRate)
currencyPair = forName + domName
spotFXRate = 90.68
tenors = ['1M']
atmVols = [21.00]
marketStrangle25DeltaVols = [0.184]
riskReversal25DeltaVols = [-5.30]
notionalCurrency = forName
atmMethod = FinFXATMMethod.FWD_DELTA_NEUTRAL
deltaMethod = FinFXDeltaMethod.SPOT_DELTA_PREM_ADJ
fxMarket = FinFXVolSurface(valuation_date,
spotFXRate,
currencyPair,
notionalCurrency,
domDiscountCurve,
forDiscountCurve,
tenors,
atmVols,
marketStrangle25DeltaVols,
riskReversal25DeltaVols,
atmMethod,
deltaMethod)
fxMarket.checkCalibration(verboseCalibration)
if PLOT_GRAPHS:
fxMarket.plotVolCurves()
def test_FinFXMktVolSurface3(verboseCalibration):
# EURUSD Example from Paper by Uwe Wystup using Tables 4
# print("EURUSD EXAMPLE WYSTUP")
valuation_date = Date(20, 1, 2009)
forName = "EUR"
domName = "USD"
forCCRate = 0.020113 # EUR
domCCRate = 0.003525 # USD
domDiscountCurve = DiscountCurveFlat(valuation_date, domCCRate)
forDiscountCurve = DiscountCurveFlat(valuation_date, forCCRate)
currencyPair = forName + domName
spotFXRate = 1.3088
tenors = ['1M']
atmVols = [21.6215]
marketStrangle25DeltaVols = [0.7375]
riskReversal25DeltaVols = [-0.50]
notionalCurrency = forName
atmMethod = FinFXATMMethod.FWD_DELTA_NEUTRAL
deltaMethod = FinFXDeltaMethod.SPOT_DELTA
fxMarket = FinFXVolSurface(valuation_date,
spotFXRate,
currencyPair,
notionalCurrency,
domDiscountCurve,
forDiscountCurve,
tenors,
atmVols,
marketStrangle25DeltaVols,
riskReversal25DeltaVols,
atmMethod,
deltaMethod)
fxMarket.checkCalibration(verboseCalibration)
if PLOT_GRAPHS:
fxMarket.plotVolCurves()
def test_FinFXVanillaOptionWystupExample2():
# Example Bloomberg Pricing at
# https://stackoverflow.com/questions/48778712/fx-vanilla-call-price-in-quantlib-doesnt-match-bloomberg
valuation_date = Date(13, 2, 2018)
expiry_date = Date(13, 2, 2019)
# In BS the FX rate is the price in domestic of one unit of foreign
# In case of EURUSD = 1.3 the domestic currency is USD and foreign is EUR
# DOM = USD , FOR = EUR
ccy1 = "EUR"
ccy2 = "USD"
ccy1CCRate = 0.0396 # EUR
ccy2CCRate = 0.0357 # USD
currencyPair = ccy1 + ccy2 # Always ccy1ccy2
spotFXRate = 0.9090
strikeFXRate = 0.9090
volatility = 0.12
notional = 1000000.0
domDiscountCurve = DiscountCurveFlat(valuation_date, ccy2CCRate)
forDiscountCurve = DiscountCurveFlat(valuation_date, ccy1CCRate)
model = FinModelBlackScholes(volatility)
# Two examples to show that changing the notional currency and notional
# keeps the value unchanged
notional = 1000000.0
callOption = FinFXVanillaOption(expiry_date, strikeFXRate, currencyPair,
FinOptionTypes.EUROPEAN_PUT, notional,
"EUR", 2)
value = callOption.value(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
delta = callOption.delta(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
testCases.header("value", "delta")
testCases.print(value, delta)
def test_FinEquityVarianceSwap():
start_date = Date(20, 3, 2018)
tenor = "3M"
strike = 0.3 * 0.3
volSwap = FinEquityVarianceSwap(start_date, tenor, strike)
valuation_date = Date(20, 3, 2018)
stock_price = 100.0
dividendYield = 0.0
dividendCurve = DiscountCurveFlat(valuation_date, dividendYield)
maturity_date = start_date.addMonths(3)
atmVol = 0.20
atmK = 100.0
skew = -0.02 / 5.0 # defined as dsigma/dK
strikes = np.linspace(50.0, 135.0, 18)
vols = volSkew(strikes, atmVol, atmK, skew)
volCurve = FinEquityVolCurve(valuation_date, maturity_date, strikes, vols)
strikeSpacing = 5.0
numCallOptions = 10
numPutOptions = 10
r = 0.05
discount_curve = DiscountCurveFlat(valuation_date, r)
useForward = False
testCases.header("LABEL", "VALUE")
k1 = volSwap.fairStrike(valuation_date, stock_price, dividendCurve,
volCurve, numCallOptions, numPutOptions,
strikeSpacing, discount_curve, useForward)
testCases.print("REPLICATION VARIANCE:", k1)
k2 = volSwap.fairStrikeApprox(valuation_date, stock_price, strikes, vols)
testCases.print("DERMAN SKEW APPROX for K:", k2)
def test_FinEquityChooserOptionMatlab():
"""https://fr.mathworks.com/help/fininst/chooserbybls.html """
valuation_date = Date(1, 6, 2007)
chooseDate = Date(31, 8, 2007)
callExpiryDate = Date(2, 12, 2007)
putExpiryDate = Date(2, 12, 2007)
callStrike = 60.0
putStrike = 60.0
stock_price = 50.0
volatility = 0.20
interestRate = 0.10
dividendYield = 0.05
model = FinModelBlackScholes(volatility)
discount_curve = DiscountCurveFlat(valuation_date, interestRate)
dividendCurve = DiscountCurveFlat(valuation_date, dividendYield)
chooserOption = FinEquityChooserOption(chooseDate,
callExpiryDate,
putExpiryDate,
callStrike,
putStrike)
v = chooserOption.value(valuation_date,
stock_price,
discount_curve,
dividendCurve,
model)
v_mc = chooserOption.valueMC(valuation_date,
stock_price,
discount_curve,
dividendCurve,
model, 20000)
v_matlab = 8.9308
testCases.header("", "", "", "", "", "")
testCases.print("FINANCEPY", v, "MATLAB", v_matlab, "MC", v_mc)
def test_FinEquityChooserOptionHaug():
""" Following example in Haug Page 130 """
valuation_date = Date(1, 1, 2015)
chooseDate = Date(2, 4, 2015)
callExpiryDate = Date(1, 7, 2015)
putExpiryDate = Date(2, 8, 2015)
callStrike = 55.0
putStrike = 48.0
stock_price = 50.0
volatility = 0.35
interestRate = 0.10
dividendYield = 0.05
model = FinModelBlackScholes(volatility)
discount_curve = DiscountCurveFlat(valuation_date, interestRate)
dividendCurve = DiscountCurveFlat(valuation_date, dividendYield)
chooserOption = FinEquityChooserOption(chooseDate,
callExpiryDate,
putExpiryDate,
callStrike,
putStrike)
v = chooserOption.value(valuation_date,
stock_price,
discount_curve,
dividendCurve,
model)
v_mc = chooserOption.valueMC(valuation_date,
stock_price,
discount_curve,
dividendCurve,
model, 20000)
v_haug = 6.0508
testCases.header("", "", "", "", "", "")
testCases.print("FINANCEPY", v, "HAUG", v_haug, "MC", v_mc)
def test_FinEquityChooserOptionDerivicom():
"""http://derivicom.com/support/finoptionsxl/index.html?complex_chooser.htm """
valuation_date = Date(1, 1, 2007)
chooseDate = Date(1, 2, 2007)
callExpiryDate = Date(1, 4, 2007)
putExpiryDate = Date(1, 5, 2007)
callStrike = 40.0
putStrike = 35.0
stock_price = 38.0
volatility = 0.20
interestRate = 0.08
dividendYield = 0.0625
model = FinModelBlackScholes(volatility)
discount_curve = DiscountCurveFlat(valuation_date, interestRate)
dividendCurve = DiscountCurveFlat(valuation_date, dividendYield)
chooserOption = FinEquityChooserOption(chooseDate,
callExpiryDate,
putExpiryDate,
callStrike,
putStrike)
v = chooserOption.value(valuation_date,
stock_price,
discount_curve,
dividendCurve,
model)
v_mc = chooserOption.valueMC(valuation_date,
stock_price,
discount_curve,
dividendCurve,
model, 20000)
v_derivicom = 1.0989
testCases.header("", "", "", "", "", "")
testCases.print("FINANCEPY", v, "DERIVICOM", v_derivicom, "MC", v_mc)
def test_FinEquityForward():
valuation_date = Date(13, 2, 2018)
expiry_date = valuation_date.addMonths(12)
stock_price = 130.0
forwardPrice = 125.0 # Locked
discountRate = 0.05
dividendRate = 0.02
###########################################################################
expiry_date = valuation_date.addMonths(12)
notional = 100.0
discount_curve = DiscountCurveFlat(valuation_date, discountRate)
dividendCurve = DiscountCurveFlat(valuation_date, dividendRate)
equityForward = FinEquityForward(expiry_date,
forwardPrice,
notional,
FinLongShort.LONG)
testCases.header("SPOT FX", "FX FWD", "VALUE_BS")
fwdPrice = equityForward.forward(valuation_date,
stock_price,
discount_curve,
dividendCurve)
fwdValue = equityForward.value(valuation_date,
stock_price,
discount_curve,
dividendCurve)
# print(stock_price, fwdPrice, fwdValue)
testCases.print(stock_price, fwdPrice, fwdValue)
def test_example():
expiry_date = Date(1, 1, 2021)
strikePrice = 105.0
optionTypeCall = FinOptionTypes.EUROPEAN_CALL
optionTypePut = FinOptionTypes.EUROPEAN_PUT
lookbackCall = FinEquityFixedLookbackOption(expiry_date, optionTypeCall, strikePrice)
lookbackPut = FinEquityFixedLookbackOption(expiry_date, optionTypePut, strikePrice)
valuation_date = Date(1, 1, 2020)
interestRate = 0.10
stock_price = 100.0
dividendYield = 0.0
stockMinMax = 100.0
discount_curve = DiscountCurveFlat(valuation_date, interestRate)
dividendCurve = DiscountCurveFlat(valuation_date, dividendYield)
volatilities = [0.30]
testCases.header("VALUE")
for vol in volatilities:
v = lookbackCall.value(valuation_date, stock_price, discount_curve, dividendCurve, vol, stockMinMax)
testCases.print(v)
def test_FinFixedOIS():
# Here I follow the example in
# https://blog.deriscope.com/index.php/en/excel-quantlib-overnight-index-swap
effective_date = Date(30, 11, 2018)
end_date = Date(30, 11, 2023)
end_date = effective_date.addMonths(60)
oisRate = 0.04
fixed_legType = FinSwapTypes.PAY
fixedFreqType = FrequencyTypes.ANNUAL
fixedDayCount = DayCountTypes.ACT_360
floatFreqType = FrequencyTypes.ANNUAL
floatDayCount = DayCountTypes.ACT_360
floatSpread = 0.0
notional = ONE_MILLION
payment_lag = 1
ois = FinOIS(effective_date, end_date, fixed_legType, oisRate,
fixedFreqType, fixedDayCount, notional, payment_lag,
floatSpread, floatFreqType, floatDayCount)
# print(ois)
valuation_date = effective_date
marketRate = 0.05
oisCurve = DiscountCurveFlat(valuation_date, marketRate,
FrequencyTypes.ANNUAL)
v = ois.value(effective_date, oisCurve)
# print(v)
# ois._fixed_leg.printValuation()
# ois._floatLeg.printValuation()
testCases.header("LABEL", "VALUE")
testCases.print("SWAP_VALUE", v)
def test_FinIborCapletHull():
# Hull Page 703, example 29.3
todayDate = Date(20, 6, 2019)
valuation_date = todayDate
maturity_date = valuation_date.addTenor("2Y")
libor_curve = DiscountCurveFlat(valuation_date,
0.070,
FrequencyTypes.QUARTERLY,
DayCountTypes.THIRTY_E_360)
k = 0.08
capFloorType = FinCapFloorTypes.CAP
capFloor = FinIborCapFloor(valuation_date,
maturity_date,
capFloorType,
k,
None,
FrequencyTypes.QUARTERLY,
DayCountTypes.THIRTY_E_360)
# Value cap using a single flat cap volatility
model = FinModelBlack(0.20)
capFloor.value(valuation_date, libor_curve, model)
# Value cap by breaking it down into caplets using caplet vols
capletStartDate = valuation_date.addTenor("1Y")
capletEndDate = capletStartDate.addTenor("3M")
vCaplet = capFloor.valueCapletFloorLet(valuation_date,
capletStartDate,
capletEndDate,
libor_curve,
model)
# Cannot match Hull due to dates being adjusted
testCases.header("CORRECT PRICE", "MODEL_PRICE")
testCases.print(517.29, vCaplet)
def test_FinSwaptionVolSurface1(verboseCalibration):
###########################################################################
if 1 == 1:
# https://fr.mathworks.com/help/fininst/pricing-a-swaption-using-the-sabr-model.html
valuation_date = Date(12, 6, 2013)
# These are 3M, 1Y, 2Y, 3Y, 4Y, 5Y, 7Y, 10Y
exerciseDates = [Date(12, 9, 2013), Date(12, 6, 2014),
Date(12, 6, 2015), Date(12, 6, 2016),
Date(12, 6, 2017), Date(12, 6, 2018),
Date(12, 6, 2020), Date(12, 6, 2023)]
# First dimension is the strike, then the expiry date
marketVolatilities = [[57.6, 53.7, 49.4, 45.6, 44.1, 41.1, 35.2, 32.0],
[46.6, 46.9, 44.8, 41.6, 39.8, 37.4, 33.4, 31.0],
[35.9, 39.3, 39.6, 37.9, 37.2, 34.7, 30.5, 28.9],
[34.1, 36.5, 37.8, 36.6, 35.0, 31.9, 28.1, 26.6],
[41.0, 41.3, 39.5, 37.8, 36.0, 32.6, 29.0, 26.0],
[45.8, 43.4, 41.9, 39.2, 36.9, 33.2, 29.6, 26.3],
[50.3, 46.9, 44.0, 40.0, 37.5, 33.8, 30.2, 27.3]]
marketVolatilities = np.array(marketVolatilities) / 100.0
# First dimension is the strike, then the expiry date
marketStrikes = [[1.00, 1.25, 1.68, 2.00, 2.26, 2.41, 2.58, 2.62],
[1.50, 1.75, 2.18, 2.50, 2.76, 2.91, 3.08, 3.12],
[2.00, 2.25, 2.68, 3.00, 3.26, 3.41, 3.58, 3.62],
[2.50, 2.75, 3.18, 3.50, 3.76, 3.91, 4.08, 4.12],
[3.00, 3.25, 3.68, 4.00, 4.26, 4.41, 4.58, 4.62],
[3.50, 3.75, 4.18, 4.50, 4.76, 4.91, 5.08, 5.12],
[4.00, 4.25, 4.68, 5.00, 5.26, 5.41, 5.58, 5.62]]
marketStrikes = np.array(marketStrikes) / 100.0
fwdSwapRates = marketStrikes[3]
atmVols = marketVolatilities[3]
rfrRate = 0.020 # USD
discount_curve = DiscountCurveFlat(valuation_date, rfrRate)
divRate = 0.010 # USD
dividendCurve = DiscountCurveFlat(valuation_date, divRate)
volFunctionType = FinVolFunctionTypes.SABR_BETA_HALF
swaptionSurface = FinSwaptionVolSurface(valuation_date,
exerciseDates,
fwdSwapRates,
marketStrikes,
marketVolatilities,
volFunctionType)
tol = 1e-4
swaptionSurface.checkCalibration(False, tol)
if 1==1: # PLOT_GRAPHS:
swaptionSurface.plotVolCurves()
def test_Bond():
import pandas as pd
path = os.path.join(os.path.dirname(__file__), './data/giltBondPrices.txt')
bondDataFrame = pd.read_csv(path, sep='\t')
bondDataFrame['mid'] = 0.5 * (bondDataFrame['bid'] + bondDataFrame['ask'])
freq_type = FrequencyTypes.SEMI_ANNUAL
settlement_date = Date(19, 9, 2012)
face = ONE_MILLION
for accrual_type in DayCountTypes:
testCases.header("MATURITY", "COUPON", "CLEAN_PRICE", "ACCD_DAYS",
"ACCRUED", "YTM")
for _, bond in bondDataFrame.iterrows():
dateString = bond['maturity']
matDatetime = dt.datetime.strptime(dateString, '%d-%b-%y')
maturityDt = fromDatetime(matDatetime)
issueDt = Date(maturityDt._d, maturityDt._m, 2000)
coupon = bond['coupon'] / 100.0
clean_price = bond['mid']
bond = Bond(issueDt, maturityDt,
coupon, freq_type, accrual_type, 100)
ytm = bond.yield_to_maturity(settlement_date, clean_price)
accrued_interest= bond._accruedInterest
accd_days = bond._accrued_days
testCases.print("%18s" % maturityDt, "%8.4f" % coupon,
"%10.4f" % clean_price, "%6.0f" % accd_days,
"%10.4f" % accrued_interest, "%8.4f" % ytm)
###########################################################################
# EXAMPLE FROM http://bondtutor.com/btchp4/topic6/topic6.htm
accrualConvention = DayCountTypes.ACT_ACT_ICMA
y = 0.062267
settlement_date = Date(19, 4, 1994)
issue_date = Date(15, 7, 1990)
maturity_date = Date(15, 7, 1997)
coupon = 0.085
face = ONE_MILLION
freq_type = FrequencyTypes.SEMI_ANNUAL
bond = Bond(issue_date, maturity_date,
coupon, freq_type, accrualConvention, face)
testCases.header("FIELD", "VALUE")
full_price = bond.full_price_from_ytm(settlement_date, y)
testCases.print("Full Price = ", full_price)
clean_price = bond.clean_price_from_ytm(settlement_date, y)
testCases.print("Clean Price = ", clean_price)
accrued_interest= bond._accruedInterest
testCases.print("Accrued = ", accrued_interest)
ytm = bond.yield_to_maturity(settlement_date, clean_price)
testCases.print("Yield to Maturity = ", ytm)
bump = 1e-4
priceBumpedUp = bond.full_price_from_ytm(settlement_date, y + bump)
testCases.print("Price Bumped Up:", priceBumpedUp)
priceBumpedDn = bond.full_price_from_ytm(settlement_date, y - bump)
testCases.print("Price Bumped Dn:", priceBumpedDn)
durationByBump = -(priceBumpedUp - full_price) / bump
testCases.print("Duration by Bump = ", durationByBump)
duration = bond.dollar_duration(settlement_date, y)
testCases.print("Dollar Duration = ", duration)
testCases.print("Duration Difference:", duration - durationByBump)
modified_duration = bond.modified_duration(settlement_date, y)
testCases.print("Modified Duration = ", modified_duration)
macauley_duration = bond.macauley_duration(settlement_date, y)
testCases.print("Macauley Duration = ", macauley_duration)
conv = bond.convexity_from_ytm(settlement_date, y)
testCases.print("Convexity = ", conv)
# ASSET SWAP SPREAD
# When the libor curve is the flat bond curve then the ASW is zero by
# definition
flatCurve = DiscountCurveFlat(settlement_date,
ytm,
FrequencyTypes.SEMI_ANNUAL)
testCases.header("FIELD", "VALUE")
clean_price = bond.clean_price_from_ytm(settlement_date, ytm)
asw = bond.asset_swap_spread(settlement_date, clean_price, flatCurve)
testCases.print("Discounted on Bond Curve ASW:", asw * 10000)
# When the libor curve is the Libor curve then the ASW is positive
libor_curve = buildIborCurve(settlement_date)
asw = bond.asset_swap_spread(settlement_date, clean_price, libor_curve)
oas = bond.option_adjusted_spread(settlement_date, clean_price, libor_curve)
testCases.print("Discounted on LIBOR Curve ASW:", asw * 10000)
testCases.print("Discounted on LIBOR Curve OAS:", oas * 10000)
p = 90.0
asw = bond.asset_swap_spread(settlement_date, p, libor_curve)
oas = bond.option_adjusted_spread(settlement_date, p, libor_curve)
testCases.print("Deep discount bond at 90 ASW:", asw * 10000)
testCases.print("Deep discount bond at 90 OAS:", oas * 10000)
p = 100.0
asw = bond.asset_swap_spread(settlement_date, p, libor_curve)
oas = bond.option_adjusted_spread(settlement_date, p, libor_curve)
testCases.print("Par bond at 100 ASW:", asw * 10000)
testCases.print("Par bond at 100 OAS:", oas * 10000)
p = 120.0
asw = bond.asset_swap_spread(settlement_date, p, libor_curve)
oas = bond.option_adjusted_spread(settlement_date, p, libor_curve)
testCases.print("Above par bond at 120 ASW:", asw * 10000)
testCases.print("Above par bond at 120 OAS:", oas * 10000)
##########################################################################
# https://data.bloomberglp.com/bat/sites/3/2017/07/SF-2017_Paul-Fjeldsted.pdf
# Page 10 TREASURY NOTE SCREENSHOT
##########################################################################
testCases.banner("BLOOMBERG US TREASURY EXAMPLE")
settlement_date = Date(21, 7, 2017)
issue_date = Date(15, 5, 2010)
maturity_date = Date(15, 5, 2027)
coupon = 0.02375
freq_type = FrequencyTypes.SEMI_ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
face = 100.0
bond = Bond(issue_date,
maturity_date,
coupon,
freq_type,
accrual_type,
face)
testCases.header("FIELD", "VALUE")
clean_price = 99.7808417
yld = bond.current_yield(clean_price)
testCases.print("Current Yield = ", yld)
ytm = bond.yield_to_maturity(settlement_date, clean_price,
FinYTMCalcType.UK_DMO)
testCases.print("UK DMO Yield To Maturity = ", ytm)
ytm = bond.yield_to_maturity(settlement_date, clean_price,
FinYTMCalcType.US_STREET)
testCases.print("US STREET Yield To Maturity = ", ytm)
ytm = bond.yield_to_maturity(settlement_date, clean_price,
FinYTMCalcType.US_TREASURY)
testCases.print("US TREASURY Yield To Maturity = ", ytm)
full_price = bond.full_price_from_ytm(settlement_date, ytm)
testCases.print("Full Price = ", full_price)
clean_price = bond.clean_price_from_ytm(settlement_date, ytm)
testCases.print("Clean Price = ", clean_price)
accrued_interest= bond._accruedInterest
testCases.print("Accrued = ", accrued_interest)
accddays = bond._accrued_days
testCases.print("Accrued Days = ", accddays)
duration = bond.dollar_duration(settlement_date, ytm)
testCases.print("Dollar Duration = ", duration)
modified_duration = bond.modified_duration(settlement_date, ytm)
testCases.print("Modified Duration = ", modified_duration)
macauley_duration = bond.macauley_duration(settlement_date, ytm)
testCases.print("Macauley Duration = ", macauley_duration)
conv = bond.convexity_from_ytm(settlement_date, ytm)
testCases.print("Convexity = ", conv)
##########################################################################
# Page 11 APPLE NOTE SCREENSHOT
##########################################################################
testCases.banner("BLOOMBERG APPLE CORP BOND EXAMPLE")
settlement_date = Date(21, 7, 2017)
issue_date = Date(13, 5, 2012)
maturity_date = Date(13, 5, 2022)
coupon = 0.027
freq_type = FrequencyTypes.SEMI_ANNUAL
accrual_type = DayCountTypes.THIRTY_E_360_ISDA
face = 100.0
bond = Bond(issue_date, maturity_date,
coupon, freq_type, accrual_type, face)
testCases.header("FIELD", "VALUE")
clean_price = 101.581564
yld = bond.current_yield(clean_price)
testCases.print("Current Yield", yld)
ytm = bond.yield_to_maturity(settlement_date, clean_price,
FinYTMCalcType.UK_DMO)
testCases.print("UK DMO Yield To Maturity", ytm)
ytm = bond.yield_to_maturity(settlement_date, clean_price,
FinYTMCalcType.US_STREET)
testCases.print("US STREET Yield To Maturity", ytm)
ytm = bond.yield_to_maturity(settlement_date, clean_price,
FinYTMCalcType.US_TREASURY)
testCases.print("US TREASURY Yield To Maturity", ytm)
full_price = bond.full_price_from_ytm(settlement_date, ytm)
testCases.print("Full Price", full_price)
clean_price = bond.clean_price_from_ytm(settlement_date, ytm)
testCases.print("Clean Price", clean_price)
accddays = bond._accrued_days
testCases.print("Accrued Days", accddays)
accrued_interest= bond._accruedInterest
testCases.print("Accrued", accrued_interest)
duration = bond.dollar_duration(settlement_date, ytm)
testCases.print("Dollar Duration", duration)
modified_duration = bond.modified_duration(settlement_date, ytm)
testCases.print("Modified Duration", modified_duration)
macauley_duration = bond.macauley_duration(settlement_date, ytm)
testCases.print("Macauley Duration", macauley_duration)
conv = bond.convexity_from_ytm(settlement_date, ytm)
testCases.print("Convexity", conv)
def test_FinBinomialTree():
stock_price = 50.0
riskFreeRate = 0.06
dividendYield = 0.04
volatility = 0.40
valuation_date = Date(1, 1, 2016)
expiry_date = Date(1, 1, 2017)
model = FinModelBlackScholes(volatility)
discount_curve = DiscountCurveFlat(valuation_date, riskFreeRate)
dividendCurve = DiscountCurveFlat(valuation_date, dividendYield)
num_stepsList = [100, 500, 1000, 2000, 5000]
strikePrice = 50.0
testCases.banner("================== EUROPEAN PUT =======================")
putOption = FinEquityVanillaOption(expiry_date, strikePrice,
FinOptionTypes.EUROPEAN_PUT)
value = putOption.value(valuation_date, stock_price, discount_curve,
dividendCurve, model)
delta = putOption.delta(valuation_date, stock_price, discount_curve,
dividendCurve, model)
gamma = putOption.gamma(valuation_date, stock_price, discount_curve,
dividendCurve, model)
theta = putOption.theta(valuation_date, stock_price, discount_curve,
dividendCurve, model)
testCases.header("BS Value", "BS Delta", "BS Gamma", "BS Theta")
testCases.print(value, delta, gamma, theta)
payoff = FinEquityTreePayoffTypes.VANILLA_OPTION
exercise = FinEquityTreeExerciseTypes.EUROPEAN
params = np.array([-1, strikePrice])
testCases.header("NumSteps", "Results", "TIME")
for num_steps in num_stepsList:
start = time.time()
tree = FinEquityBinomialTree()
results = tree.value(stock_price, discount_curve, dividendCurve,
volatility, num_steps, valuation_date, payoff,
expiry_date, payoff, exercise, params)
end = time.time()
duration = end - start
testCases.print(num_steps, results, duration)
testCases.banner("================== AMERICAN PUT =======================")
payoff = FinEquityTreePayoffTypes.VANILLA_OPTION
exercise = FinEquityTreeExerciseTypes.AMERICAN
params = np.array([-1, strikePrice])
testCases.header("NumSteps", "Results", "TIME")
for num_steps in num_stepsList:
start = time.time()
tree = FinEquityBinomialTree()
results = tree.value(stock_price, discount_curve, dividendCurve,
volatility, num_steps, valuation_date, payoff,
expiry_date, payoff, exercise, params)
end = time.time()
duration = end - start
testCases.print(num_steps, results, duration)
testCases.banner(
"================== EUROPEAN CALL =======================")
callOption = FinEquityVanillaOption(expiry_date, strikePrice,
FinOptionTypes.EUROPEAN_CALL)
value = callOption.value(valuation_date, stock_price, discount_curve,
dividendCurve, model)
delta = callOption.delta(valuation_date, stock_price, discount_curve,
dividendCurve, model)
gamma = callOption.gamma(valuation_date, stock_price, discount_curve,
dividendCurve, model)
theta = callOption.theta(valuation_date, stock_price, discount_curve,
dividendCurve, model)
testCases.header("BS Value", "BS Delta", "BS Gamma", "BS Theta")
testCases.print(value, delta, gamma, theta)
payoff = FinEquityTreePayoffTypes.VANILLA_OPTION
exercise = FinEquityTreeExerciseTypes.EUROPEAN
params = np.array([1.0, strikePrice])
testCases.header("NumSteps", "Results", "TIME")
for num_steps in num_stepsList:
start = time.time()
tree = FinEquityBinomialTree()
results = tree.value(stock_price, discount_curve, dividendCurve,
volatility, num_steps, valuation_date, payoff,
expiry_date, payoff, exercise, params)
end = time.time()
duration = end - start
testCases.print(num_steps, results, duration)
testCases.banner(
"================== AMERICAN CALL =======================")
payoff = FinEquityTreePayoffTypes.VANILLA_OPTION
exercise = FinEquityTreeExerciseTypes.AMERICAN
params = np.array([1.0, strikePrice])
testCases.header("NumSteps", "Results", "TIME")
for num_steps in num_stepsList:
start = time.time()
tree = FinEquityBinomialTree()
results = tree.value(stock_price, discount_curve, dividendCurve,
volatility, num_steps, valuation_date, payoff,
expiry_date, payoff, exercise, params)
end = time.time()
duration = end - start
testCases.print(num_steps, results, duration)
def test_FinIborBermudanSwaptionBKModel():
""" Replicate examples in paper by Leif Andersen which can be found at
file:///C:/Users/Dominic/Downloads/SSRN-id155208.pdf """
valuation_date = Date(1, 1, 2011)
settlement_date = valuation_date
exerciseDate = settlement_date.addYears(1)
swapMaturityDate = settlement_date.addYears(4)
swapFixedCoupon = 0.060
swapFixedFrequencyType = FrequencyTypes.SEMI_ANNUAL
swapFixedDayCountType = DayCountTypes.ACT_365F
libor_curve = DiscountCurveFlat(valuation_date, 0.0625,
FrequencyTypes.SEMI_ANNUAL,
DayCountTypes.ACT_365F)
fwdPAYSwap = FinIborSwap(exerciseDate, swapMaturityDate, FinSwapTypes.PAY,
swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fwdSwapValue = fwdPAYSwap.value(settlement_date, libor_curve, libor_curve)
testCases.header("LABEL", "VALUE")
testCases.print("FWD SWAP VALUE", fwdSwapValue)
# fwdPAYSwap.printFixedLegPV()
# Now we create the European swaptions
fixed_legType = FinSwapTypes.PAY
europeanSwaptionPay = FinIborSwaption(settlement_date, exerciseDate,
swapMaturityDate, fixed_legType,
swapFixedCoupon,
swapFixedFrequencyType,
swapFixedDayCountType)
fixed_legType = FinSwapTypes.RECEIVE
europeanSwaptionRec = FinIborSwaption(settlement_date, exerciseDate,
swapMaturityDate, fixed_legType,
swapFixedCoupon,
swapFixedFrequencyType,
swapFixedDayCountType)
###########################################################################
###########################################################################
###########################################################################
# BLACK'S MODEL
###########################################################################
###########################################################################
###########################################################################
testCases.banner("======= ZERO VOLATILITY ========")
model = FinModelBlack(0.0000001)
testCases.print("Black Model", model._volatility)
valuePay = europeanSwaptionPay.value(settlement_date, libor_curve, model)
testCases.print("EUROPEAN BLACK PAY VALUE ZERO VOL:", valuePay)
valueRec = europeanSwaptionRec.value(settlement_date, libor_curve, model)
testCases.print("EUROPEAN BLACK REC VALUE ZERO VOL:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner("======= 20%% BLACK VOLATILITY ========")
model = FinModelBlack(0.20)
testCases.print("Black Model", model._volatility)
valuePay = europeanSwaptionPay.value(settlement_date, libor_curve, model)
testCases.print("EUROPEAN BLACK PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(settlement_date, libor_curve, model)
testCases.print("EUROPEAN BLACK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
###########################################################################
###########################################################################
# BK MODEL
###########################################################################
###########################################################################
###########################################################################
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("==================== BK MODEL =========================")
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("======= 0% VOLATILITY EUROPEAN SWAPTION BK MODEL ======")
# Used BK with constant short-rate volatility
sigma = 0.000000001
a = 0.01
numTimeSteps = 100
model = FinModelRatesBK(sigma, a, numTimeSteps)
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BK PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 20% VOLATILITY EUROPEAN SWAPTION BK MODEL ========")
# Used BK with constant short-rate volatility
sigma = 0.20
a = 0.01
model = FinModelRatesBK(sigma, a, numTimeSteps)
testCases.banner("BK MODEL SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BK PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but only allow European exercise
fixed_legType = FinSwapTypes.PAY
exerciseType = FinExerciseTypes.EUROPEAN
bermudanSwaptionPay = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_legType = FinSwapTypes.RECEIVE
exerciseType = FinExerciseTypes.EUROPEAN
bermudanSwaptionRec = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= 0% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE BK MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
a = 0.01
model = FinModelRatesBK(sigma, a, numTimeSteps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 20% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE BK MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.2
a = 0.01
model = FinModelRatesBK(sigma, a, numTimeSteps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but allow Bermudan exercise
###########################################################################
fixed_legType = FinSwapTypes.PAY
exerciseType = FinExerciseTypes.BERMUDAN
bermudanSwaptionPay = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_legType = FinSwapTypes.RECEIVE
exerciseType = FinExerciseTypes.BERMUDAN
bermudanSwaptionRec = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= ZERO VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE BK MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
a = 0.01
model = FinModelRatesBK(sigma, a, numTimeSteps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 20% VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE BK MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.20
a = 0.01
model = FinModelRatesBK(sigma, a, numTimeSteps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
###########################################################################
###########################################################################
# BDT MODEL
###########################################################################
###########################################################################
###########################################################################
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("======================= BDT MODEL =====================")
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("====== 0% VOLATILITY EUROPEAN SWAPTION BDT MODEL ======")
# Used BK with constant short-rate volatility
sigma = 0.00001
numTimeSteps = 200
model = FinModelRatesBDT(sigma, numTimeSteps)
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BDT PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner("===== 20% VOLATILITY EUROPEAN SWAPTION BDT MODEL ======")
# Used BK with constant short-rate volatility
sigma = 0.20
a = 0.01
model = FinModelRatesBDT(sigma, numTimeSteps)
testCases.banner("BDT MODEL SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BDT PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but only allow European exercise
fixed_legType = FinSwapTypes.PAY
exerciseType = FinExerciseTypes.EUROPEAN
bermudanSwaptionPay = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_legType = FinSwapTypes.RECEIVE
bermudanSwaptionRec = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= 0% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE BDT MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
model = FinModelRatesBDT(sigma, numTimeSteps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 20% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE BDT MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.2
model = FinModelRatesBDT(sigma, numTimeSteps)
testCases.banner("BDT MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but allow Bermudan exercise
###########################################################################
fixed_legType = FinSwapTypes.PAY
exerciseType = FinExerciseTypes.BERMUDAN
bermudanSwaptionPay = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_legType = FinSwapTypes.RECEIVE
bermudanSwaptionRec = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= ZERO VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE BDT MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
a = 0.01
model = FinModelRatesBDT(sigma, numTimeSteps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 20% VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE BDT MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.20
a = 0.01
model = FinModelRatesBDT(sigma, numTimeSteps)
# print("BDT MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
###########################################################################
###########################################################################
# BDT MODEL
###########################################################################
###########################################################################
###########################################################################
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("======================= HW MODEL ======================")
testCases.banner("=======================================================")
testCases.banner("=======================================================")
testCases.banner("====== 0% VOLATILITY EUROPEAN SWAPTION HW MODEL ======")
sigma = 0.0000001
a = 0.1
numTimeSteps = 200
model = FinModelRatesHW(sigma, a, numTimeSteps)
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN HW PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN HW REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner("===== 20% VOLATILITY EUROPEAN SWAPTION BDT MODEL ======")
# Used BK with constant short-rate volatility
sigma = 0.01
a = 0.01
model = FinModelRatesHW(sigma, a, numTimeSteps)
testCases.banner("HW MODEL SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = europeanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN HW PAY VALUE:", valuePay)
valueRec = europeanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("EUROPEAN HW REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but only allow European exercise
fixed_legType = FinSwapTypes.PAY
exerciseType = FinExerciseTypes.EUROPEAN
bermudanSwaptionPay = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_legType = FinSwapTypes.RECEIVE
bermudanSwaptionRec = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= 0% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE HW MODEL ========"
)
sigma = 0.000001
model = FinModelRatesHW(sigma, a, numTimeSteps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 100bp VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE HW MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.01
model = FinModelRatesHW(sigma, a, numTimeSteps)
testCases.banner("BDT MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
###########################################################################
# Now we create the Bermudan swaptions but allow Bermudan exercise
###########################################################################
fixed_legType = FinSwapTypes.PAY
exerciseType = FinExerciseTypes.BERMUDAN
bermudanSwaptionPay = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_legType = FinSwapTypes.RECEIVE
bermudanSwaptionRec = FinIborBermudanSwaption(
settlement_date, exerciseDate, swapMaturityDate, fixed_legType,
exerciseType, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= ZERO VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE HW MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
a = 0.01
model = FinModelRatesHW(sigma, a, numTimeSteps)
testCases.banner("HW MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
testCases.banner(
"======= 100bps VOLATILITY BERMUDAN SWAPTION BERMUDAN EXERCISE HW MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.01
a = 0.01
model = FinModelRatesHW(sigma, a, numTimeSteps)
testCases.banner("HW MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudanSwaptionPay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW PAY VALUE:", valuePay)
valueRec = bermudanSwaptionRec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
def test_FinEquityRainbowOption():
# import matplotlib.pyplot as plt
valuation_date = Date(1, 1, 2015)
expiry_date = Date(1, 1, 2016)
interestRate = 0.05
discount_curve = DiscountCurveFlat(valuation_date, interestRate)
numAssets = 2
volatilities = np.ones(numAssets) * 0.3
dividend_yields = np.ones(numAssets) * 0.01
dividendCurves = []
for q in dividend_yields:
dividendCurve = DiscountCurveFlat(valuation_date, q)
dividendCurves.append(dividendCurve)
stock_prices = np.ones(numAssets) * 100
num_pathsList = [10000]
corrList = np.linspace(0.0, 0.999999, 6)
strike = 100.0
testCases.banner(
"===================================================================")
testCases.banner(" CALL ON MAXIMUM")
testCases.banner(
"===================================================================")
payoffType = FinEquityRainbowOptionTypes.CALL_ON_MAXIMUM
payoffParams = [strike]
rainbowOption = FinEquityRainbowOption(expiry_date, payoffType,
payoffParams, numAssets)
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(numAssets) * sqrt(correlation)
corrMatrix = betaVectorToCorrMatrix(betas)
for num_paths in num_pathsList:
start = time.time()
v = rainbowOption.value(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix)
v_MC = rainbowOption.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "CALL ON MAX Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "CALL ON MAX Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
##########################################################################
testCases.banner(
"===================================================================")
testCases.banner(" CALL ON MINIMUM")
testCases.banner(
"===================================================================")
payoffType = FinEquityRainbowOptionTypes.CALL_ON_MINIMUM
payoffParams = [strike]
rainbowOption = FinEquityRainbowOption(expiry_date, payoffType,
payoffParams, numAssets)
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(numAssets) * sqrt(correlation)
corrMatrix = betaVectorToCorrMatrix(betas)
for num_paths in num_pathsList:
start = time.time()
v = rainbowOption.value(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix)
v_MC = rainbowOption.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "CALL ON MIN Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "CALL ON MIN Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
###############################################################################
testCases.banner(
"===================================================================")
testCases.banner(" PUT ON MAXIMUM")
testCases.banner(
"===================================================================")
payoffType = FinEquityRainbowOptionTypes.PUT_ON_MAXIMUM
payoffParams = [strike]
rainbowOption = FinEquityRainbowOption(expiry_date, payoffType,
payoffParams, numAssets)
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(numAssets) * sqrt(correlation)
corrMatrix = betaVectorToCorrMatrix(betas)
for num_paths in num_pathsList:
start = time.time()
v = rainbowOption.value(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix)
v_MC = rainbowOption.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "PUT ON MAX Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "PUT ON MAX Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
##########################################################################
testCases.banner(
"===================================================================")
testCases.banner(" PUT ON MINIMUM")
testCases.banner(
"===================================================================")
payoffType = FinEquityRainbowOptionTypes.PUT_ON_MINIMUM
payoffParams = [strike]
rainbowOption = FinEquityRainbowOption(expiry_date, payoffType,
payoffParams, numAssets)
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(numAssets) * sqrt(correlation)
corrMatrix = betaVectorToCorrMatrix(betas)
for num_paths in num_pathsList:
start = time.time()
v = rainbowOption.value(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix)
v_MC = rainbowOption.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "PUT ON MIN Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "PUT ON MIN Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
##########################################################################
numAssets = 2
volatilities = np.ones(numAssets) * 0.3
dividend_yields = np.ones(numAssets) * 0.01
stock_prices = np.ones(numAssets) * 100
strike = 100.0
correlation = 0.50
testCases.banner(
"===================================================================")
testCases.banner(" CALL ON 1st")
testCases.banner(
"===================================================================")
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(numAssets) * sqrt(correlation)
corrMatrix = betaVectorToCorrMatrix(betas)
for num_paths in num_pathsList:
payoffType1 = FinEquityRainbowOptionTypes.CALL_ON_MAXIMUM
payoffParams1 = [strike]
rainbowOption1 = FinEquityRainbowOption(expiry_date, payoffType1,
payoffParams1, numAssets)
payoffType2 = FinEquityRainbowOptionTypes.CALL_ON_NTH
payoffParams2 = [1, strike]
rainbowOption2 = FinEquityRainbowOption(expiry_date, payoffType2,
payoffParams2, numAssets)
start = time.time()
v = rainbowOption1.value(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix)
v_MC = rainbowOption2.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "CALL ON MAX Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "CALL ON 1st Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
testCases.banner(
"===================================================================")
testCases.banner(" CALL ON 2nd")
testCases.banner(
"===================================================================")
rainboxOptionValues = []
rainbowOptionValuesMC = []
testCases.header("NUMPATHS", "CORRELATION", "VALUE", "VALUE_MC", "TIME")
for correlation in corrList:
betas = np.ones(numAssets) * sqrt(correlation)
corrMatrix = betaVectorToCorrMatrix(betas)
for num_paths in num_pathsList:
payoffType1 = FinEquityRainbowOptionTypes.CALL_ON_MINIMUM
payoffParams1 = [strike]
rainbowOption1 = FinEquityRainbowOption(expiry_date, payoffType1,
payoffParams1, numAssets)
payoffType2 = FinEquityRainbowOptionTypes.CALL_ON_NTH
payoffParams2 = [2, strike]
rainbowOption2 = FinEquityRainbowOption(expiry_date, payoffType2,
payoffParams2, numAssets)
start = time.time()
v = rainbowOption1.value(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix)
v_MC = rainbowOption2.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, v, v_MC, duration)
rainboxOptionValues.append(v)
rainbowOptionValuesMC.append(v_MC)
# plt.figure(figsize=(10,8))
# plt.plot(corrList, rainboxOptionValues, color = 'r', label = "CALL ON MIN Rainbow Option Analytical")
# plt.plot(corrList, rainbowOptionValuesMC, 'o', color = 'b', label = "CALL ON 2nd Rainbow Option MC")
# plt.xlabel("Correlation")
# plt.legend(loc='best')
testCases.banner(
"===================================================================")
testCases.banner(" CALL ON 1-5")
testCases.banner(
"===================================================================")
rainboxOptionValues = []
rainbowOptionValuesMC = []
num_paths = 10000
numAssets = 5
volatilities = np.ones(numAssets) * 0.3
dividend_yields = np.ones(numAssets) * 0.01
stock_prices = np.ones(numAssets) * 100
dividendCurves = []
for q in dividend_yields:
dividendCurve = DiscountCurveFlat(valuation_date, q)
dividendCurves.append(dividendCurve)
# plt.figure(figsize=(10,8))
testCases.header("NUMPATHS", "CORRELATION", "NTD", "VALUE", "VALUE_MC",
"TIME")
for n in [1, 2, 3, 4, 5]:
rainboxOptionValues = []
rainbowOptionValuesMC = []
payoffType2 = FinEquityRainbowOptionTypes.CALL_ON_NTH
payoffParams2 = [n, strike]
rainbowOption2 = FinEquityRainbowOption(expiry_date, payoffType2,
payoffParams2, numAssets)
for correlation in corrList:
betas = np.ones(numAssets) * sqrt(correlation)
corrMatrix = betaVectorToCorrMatrix(betas)
start = time.time()
v_MC = rainbowOption2.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, n, v, v_MC, duration)
rainbowOptionValuesMC.append(v_MC)
# plt.plot(corrList, rainbowOptionValuesMC, 'o-', label = "CALL Rainbow Option MC NTH = " + str(n))
# plt.xlabel("Correlation")
# plt.legend(loc='best')
testCases.banner(
"===================================================================")
testCases.banner(" PUT ON 1-5")
testCases.banner(
"===================================================================")
rainboxOptionValues = []
rainbowOptionValuesMC = []
num_paths = 10000
numAssets = 5
volatilities = np.ones(numAssets) * 0.3
dividend_yields = np.ones(numAssets) * 0.01
stock_prices = np.ones(numAssets) * 100
# plt.figure(figsize=(10,8))
testCases.header("NUMPATHS", "CORRELATION", "NTD", "VALUE", "VALUE_MC",
"TIME")
for n in [1, 2, 3, 4, 5]:
rainboxOptionValues = []
rainbowOptionValuesMC = []
payoffType2 = FinEquityRainbowOptionTypes.PUT_ON_NTH
payoffParams2 = [n, strike]
rainbowOption2 = FinEquityRainbowOption(expiry_date, payoffType2,
payoffParams2, numAssets)
for correlation in corrList:
betas = np.ones(numAssets) * sqrt(correlation)
corrMatrix = betaVectorToCorrMatrix(betas)
start = time.time()
v_MC = rainbowOption2.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, correlation, n, v, v_MC, duration)
rainbowOptionValuesMC.append(v_MC)
def test_FinFXVanillaOptionHullExample():
# Example from Hull 4th edition page 284
valuation_date = Date(1, 1, 2015)
expiry_date = valuation_date.addMonths(4)
spotFXRate = 1.60
volatility = 0.1411
domInterestRate = 0.08
forInterestRate = 0.11
model = FinModelBlackScholes(volatility)
domDiscountCurve = DiscountCurveFlat(valuation_date, domInterestRate)
forDiscountCurve = DiscountCurveFlat(valuation_date, forInterestRate)
num_pathsList = [10000, 20000, 40000, 80000, 160000, 320000]
testCases.header("NUMPATHS", "VALUE_BS", "VALUE_MC", "TIME")
strikeFXRate = 1.60
for num_paths in num_pathsList:
callOption = FinFXVanillaOption(expiry_date, strikeFXRate, "EURUSD",
FinOptionTypes.EUROPEAN_CALL, 1000000,
"USD")
value = callOption.value(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
start = time.time()
valueMC = callOption.valueMC(valuation_date, spotFXRate,
domDiscountCurve, forDiscountCurve, model,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, value, valueMC, duration)
##########################################################################
spotFXRates = np.arange(100, 200, 10)
spotFXRates = spotFXRates / 100.0
num_paths = 100000
testCases.header("NUMPATHS", "CALL_VALUE_BS", "CALL_VALUE_MC", "TIME")
for spotFXRate in spotFXRates:
callOption = FinFXVanillaOption(expiry_date, strikeFXRate, "EURUSD",
FinOptionTypes.EUROPEAN_CALL, 1000000,
"USD")
value = callOption.value(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
start = time.time()
valueMC = callOption.valueMC(valuation_date, spotFXRate,
domDiscountCurve, forDiscountCurve, model,
num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, value, valueMC, duration)
##########################################################################
spotFXRates = np.arange(100, 200, 10) / 100.0
num_paths = 100000
testCases.header("SPOT FX RATE", "PUT_VALUE_BS", "PUT_VALUE_MC", "TIME")
for spotFXRate in spotFXRates:
putOption = FinFXVanillaOption(expiry_date, strikeFXRate, "EURUSD",
FinOptionTypes.EUROPEAN_PUT, 1000000,
"USD")
value = putOption.value(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
start = time.time()
valueMC = putOption.valueMC(valuation_date, spotFXRate,
domDiscountCurve, forDiscountCurve, model,
num_paths)
end = time.time()
duration = end - start
testCases.print(spotFXRate, value, valueMC, duration)
##########################################################################
spotFXRates = np.arange(100, 200, 10) / 100.0
testCases.header("SPOT FX RATE", "CALL_VALUE_BS", "DELTA_BS", "VEGA_BS",
"THETA_BS", "RHO_BS")
for spotFXRate in spotFXRates:
callOption = FinFXVanillaOption(expiry_date, strikeFXRate, "EURUSD",
FinOptionTypes.EUROPEAN_CALL, 1000000,
"USD")
value = callOption.value(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
delta = callOption.delta(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
vega = callOption.vega(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
theta = callOption.theta(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
# callOption.rho(valuation_date,stock_price, interestRate,
# dividendYield, modelType, modelParams)
rho = 999
testCases.print(spotFXRate, value, delta, vega, theta, rho)
testCases.header("SPOT FX RATE", "PUT_VALUE_BS", "DELTA_BS", "VEGA_BS",
"THETA_BS", "RHO_BS")
for spotFXRate in spotFXRates:
putOption = FinFXVanillaOption(expiry_date, strikeFXRate, "EURUSD",
FinOptionTypes.EUROPEAN_PUT, 1000000,
"USD")
value = putOption.value(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
delta = putOption.delta(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
vega = putOption.vega(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
theta = putOption.theta(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)
# putOption.rho(valuation_date,stock_price, interestRate, dividendYield,
# modelType, modelParams)
rho = 999
testCases.print(spotFXRate, value, delta, vega, theta, rho)
##########################################################################
testCases.header("SPOT FX RATE", "VALUE_BS", "VOL_IN", "IMPLD_VOL")
spotFXRates = np.arange(100, 200, 10) / 100.0
for spotFXRate in spotFXRates:
callOption = FinFXVanillaOption(expiry_date, strikeFXRate, "EURUSD",
FinOptionTypes.EUROPEAN_CALL, 1000000,
"USD")
value = callOption.value(valuation_date, spotFXRate, domDiscountCurve,
forDiscountCurve, model)['v']
impliedVol = callOption.impliedVolatility(valuation_date, spotFXRate,
domDiscountCurve,
forDiscountCurve, value)
testCases.print(spotFXRate, value, volatility, impliedVol)
def test_FinEquityVolSurface(verboseCalibration):
valuation_date = Date(11, 1, 2021)
stock_price = 3800.0 # Check
expiry_dates = [
Date(11, 2, 2021),
Date(11, 3, 2021),
Date(11, 4, 2021),
Date(11, 7, 2021),
Date(11, 10, 2021),
Date(11, 1, 2022),
Date(11, 1, 2023)
]
strikes = np.array([3037, 3418, 3608, 3703, 3798, 3893, 3988, 4178, 4557])
volSurface = [
[42.94, 31.30, 25.88, 22.94, 19.72, 16.90, 15.31, 17.54, 25.67],
[37.01, 28.25, 24.19, 21.93, 19.57, 17.45, 15.89, 15.34, 21.15],
[34.68, 27.38, 23.82, 21.85, 19.83, 17.98, 16.52, 15.31, 18.94],
[31.41, 26.25, 23.51, 22.05, 20.61, 19.25, 18.03, 16.01, 15.90],
[29.91, 25.58, 23.21, 22.01, 20.83, 19.70, 18.62, 16.63, 14.94],
[29.26, 25.24, 23.03, 21.91, 20.81, 19.73, 18.69, 16.76, 14.63],
[27.59, 24.33, 22.72, 21.93, 21.17, 20.43, 19.71, 18.36, 16.26]
]
volSurface = np.array(volSurface)
volSurface = volSurface / 100.0
r = 0.020 # USD
discount_curve = DiscountCurveFlat(valuation_date, r)
q = 0.010 # USD
dividendCurve = DiscountCurveFlat(valuation_date, q)
volFunctionType = FinVolFunctionTypes.SVI
equitySurface = FinEquityVolSurface(valuation_date, stock_price,
discount_curve, dividendCurve,
expiry_dates, strikes, volSurface,
volFunctionType)
# tol = 1e-4
# equitySurface.checkCalibration(False, tol)
if 1 == 0: # PLOT_GRAPHS:
equitySurface.plotVolCurves()
plt.figure()
mins = strikes[0] * 0.5
maxs = strikes[-1] * 1.5
dbns = equitySurface.impliedDbns(mins, maxs, 1000)
for i in range(0, len(dbns)):
expiry_dateStr = str(equitySurface._expiry_dates[i])
plt.plot(dbns[i]._x, dbns[i]._densitydx, label=expiry_dateStr)
plt.title(volFunctionType)
plt.legend()
print("SUM:", dbns[i].sum())
deltas = np.linspace(0.10, 0.90, 9)
testCases.header("EXPIRY", "DELTA", "VOL", "STRIKE")
for expiry_date in expiry_dates:
for delta in deltas:
vol = equitySurface.volatilityFromDeltaDate(delta, expiry_date)
testCases.print(expiry_date, delta, vol[0], vol[1])
def test_FinEquityBasketOption():
import time
valuation_date = Date(1, 1, 2015)
expiry_date = Date(1, 1, 2016)
volatility = 0.30
interestRate = 0.05
discount_curve = DiscountCurveFlat(valuation_date, interestRate)
##########################################################################
# Homogeneous Basket
##########################################################################
numAssets = 5
volatilities = np.ones(numAssets) * volatility
dividend_yields = np.ones(numAssets) * 0.01
stock_prices = np.ones(numAssets) * 100
dividendCurves = []
for q in dividend_yields:
dividendCurve = DiscountCurveFlat(valuation_date, q)
dividendCurves.append(dividendCurve)
betaList = np.linspace(0.0, 0.999999, 11)
testCases.header("NumPaths", "Beta", "Value", "ValueMC", "TIME")
for beta in betaList:
for num_paths in [10000]:
callOption = FinEquityBasketOption(expiry_date, 100.0,
FinOptionTypes.EUROPEAN_CALL,
numAssets)
betas = np.ones(numAssets) * beta
corrMatrix = betaVectorToCorrMatrix(betas)
start = time.time()
v = callOption.value(valuation_date, stock_prices, discount_curve,
dividendCurves, volatilities, corrMatrix)
vMC = callOption.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, beta, v, vMC, duration)
##########################################################################
# INHomogeneous Basket
##########################################################################
numAssets = 5
volatilities = np.array([0.3, 0.2, 0.25, 0.22, 0.4])
dividend_yields = np.array([0.01, 0.02, 0.04, 0.01, 0.02])
stock_prices = np.array([100, 105, 120, 100, 90])
dividendCurves = []
for q in dividend_yields:
dividendCurve = DiscountCurveFlat(valuation_date, q)
dividendCurves.append(dividendCurve)
betaList = np.linspace(0.0, 0.999999, 11)
testCases.header("NumPaths", "Beta", "Value", "ValueMC", "TIME")
for beta in betaList:
for num_paths in [10000]:
callOption = FinEquityBasketOption(expiry_date, 100.0,
FinOptionTypes.EUROPEAN_CALL,
numAssets)
betas = np.ones(numAssets) * beta
corrMatrix = betaVectorToCorrMatrix(betas)
start = time.time()
v = callOption.value(valuation_date, stock_prices, discount_curve,
dividendCurves, volatilities, corrMatrix)
vMC = callOption.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, beta, v, vMC, duration)
##########################################################################
# Homogeneous Basket
##########################################################################
numAssets = 5
volatilities = np.ones(numAssets) * volatility
dividend_yields = np.ones(numAssets) * 0.01
stock_prices = np.ones(numAssets) * 100
betaList = np.linspace(0.0, 0.999999, 11)
dividendCurves = []
for q in dividend_yields:
dividendCurve = DiscountCurveFlat(valuation_date, q)
dividendCurves.append(dividendCurve)
testCases.header("NumPaths", "Beta", "Value", "ValueMC", "TIME")
for beta in betaList:
for num_paths in [10000]:
callOption = FinEquityBasketOption(expiry_date, 100.0,
FinOptionTypes.EUROPEAN_PUT,
numAssets)
betas = np.ones(numAssets) * beta
corrMatrix = betaVectorToCorrMatrix(betas)
start = time.time()
v = callOption.value(valuation_date, stock_prices, discount_curve,
dividendCurves, volatilities, corrMatrix)
vMC = callOption.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, beta, v, vMC, duration)
##########################################################################
# INHomogeneous Basket
##########################################################################
numAssets = 5
volatilities = np.array([0.3, 0.2, 0.25, 0.22, 0.4])
dividend_yields = np.array([0.01, 0.02, 0.04, 0.01, 0.02])
stock_prices = np.array([100, 105, 120, 100, 90])
betaList = np.linspace(0.0, 0.999999, 11)
dividendCurves = []
for q in dividend_yields:
dividendCurve = DiscountCurveFlat(valuation_date, q)
dividendCurves.append(dividendCurve)
testCases.header("NumPaths", "Beta", "Value", "ValueMC", "TIME")
for beta in betaList:
for num_paths in [10000]:
callOption = FinEquityBasketOption(expiry_date, 100.0,
FinOptionTypes.EUROPEAN_PUT,
numAssets)
betas = np.ones(numAssets) * beta
corrMatrix = betaVectorToCorrMatrix(betas)
start = time.time()
v = callOption.value(valuation_date, stock_prices, discount_curve,
dividendCurves, volatilities, corrMatrix)
vMC = callOption.valueMC(valuation_date, stock_prices,
discount_curve, dividendCurves,
volatilities, corrMatrix, num_paths)
end = time.time()
duration = end - start
testCases.print(num_paths, beta, v, vMC, duration)
def testFinModelBlackScholes():
valuation_date = Date(8, 5, 2015)
expiry_date = Date(15, 1, 2016)
strikePrice = 130.0
stock_price = 127.62
volatility = 0.20
interestRate = 0.001
dividendYield = 0.0163
optionType = FinOptionTypes.AMERICAN_CALL
euOptionType = FinOptionTypes.EUROPEAN_CALL
amOption = FinEquityAmericanOption(expiry_date, strikePrice, optionType)
ameuOption = FinEquityAmericanOption(expiry_date, strikePrice,
euOptionType)
euOption = FinEquityVanillaOption(expiry_date, strikePrice, euOptionType)
discount_curve = DiscountCurveFlat(valuation_date, interestRate,
FrequencyTypes.CONTINUOUS,
DayCountTypes.ACT_365F)
dividendCurve = DiscountCurveFlat(valuation_date, dividendYield,
FrequencyTypes.CONTINUOUS,
DayCountTypes.ACT_365F)
num_steps_per_year = 400
modelTree = FinModelBlackScholes(volatility,
FinModelBlackScholesTypes.CRR_TREE,
num_steps_per_year)
v = amOption.value(valuation_date, stock_price, discount_curve,
dividendCurve, modelTree)
# print(v)
modelApprox = FinModelBlackScholes(volatility,
FinModelBlackScholesTypes.BARONE_ADESI)
v = amOption.value(valuation_date, stock_price, discount_curve,
dividendCurve, modelApprox)
# print(v)
v = ameuOption.value(valuation_date, stock_price, discount_curve,
dividendCurve, modelTree)
# print(v)
v = euOption.value(valuation_date, stock_price, discount_curve,
dividendCurve, modelTree)
# print(v)
amTreeValue = []
amBAWValue = []
euTreeValue = []
euAnalValue = []
volatility = 0.20
def test_BondOptionZEROVOLConvergence():
# Build discount curve
settlement_date = Date(1, 9, 2019)
rate = 0.05
discount_curve = DiscountCurveFlat(settlement_date, rate,
FrequencyTypes.ANNUAL)
# Bond details
issue_date = Date(1, 9, 2014)
maturity_date = Date(1, 9, 2025)
coupon = 0.06
freq_type = FrequencyTypes.ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
# Option Details
expiry_date = Date(1, 12, 2021)
face = 100.0
dfExpiry = discount_curve.df(expiry_date)
fwdCleanValue = bond.clean_price_from_discount_curve(
expiry_date, discount_curve)
# fwdFullValue = bond.full_price_from_discount_curve(expiry_date, discount_curve)
# print("BOND FwdCleanBondPx", fwdCleanValue)
# print("BOND FwdFullBondPx", fwdFullValue)
# print("BOND Accrued:", bond._accruedInterest)
spotCleanValue = bond.clean_price_from_discount_curve(
settlement_date, discount_curve)
testCases.header("STRIKE", "STEPS", "CALL_INT", "CALL_INT_PV", "CALL_EUR",
"CALL_AMER", "PUT_INT", "PUT_INT_PV", "PUT_EUR",
"PUT_AMER")
numTimeSteps = range(100, 1000, 100)
strikePrices = [90, 100, 110, 120]
for strikePrice in strikePrices:
callIntrinsic = max(spotCleanValue - strikePrice, 0)
putIntrinsic = max(strikePrice - spotCleanValue, 0)
callIntrinsicPV = max(fwdCleanValue - strikePrice, 0) * dfExpiry
putIntrinsicPV = max(strikePrice - fwdCleanValue, 0) * dfExpiry
for num_steps in numTimeSteps:
sigma = 0.0000001
a = 0.1
model = FinModelRatesHW(sigma, a, num_steps)
optionType = FinOptionTypes.EUROPEAN_CALL
bondOption1 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
v1 = bondOption1.value(settlement_date, discount_curve, model)
optionType = FinOptionTypes.AMERICAN_CALL
bondOption2 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
v2 = bondOption2.value(settlement_date, discount_curve, model)
optionType = FinOptionTypes.EUROPEAN_PUT
bondOption3 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
v3 = bondOption3.value(settlement_date, discount_curve, model)
optionType = FinOptionTypes.AMERICAN_PUT
bondOption4 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
v4 = bondOption4.value(settlement_date, discount_curve, model)
testCases.print(strikePrice, num_steps, callIntrinsic,
callIntrinsicPV, v1, v2, putIntrinsic,
putIntrinsicPV, v3, v4)
def test_BondOptionAmericanConvergenceTWO():
# Build discount curve
settlement_date = Date(1, 12, 2019)
discount_curve = DiscountCurveFlat(settlement_date, 0.05)
# Bond details
issue_date = Date(1, 12, 2015)
maturity_date = settlement_date.addTenor("10Y")
coupon = 0.05
freq_type = FrequencyTypes.SEMI_ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
expiry_date = settlement_date.addTenor("18m")
face = 100.0
spotValue = bond.clean_price_from_discount_curve(settlement_date,
discount_curve)
testCases.header("LABEL", "VALUE")
testCases.print("BOND PRICE", spotValue)
testCases.header("TIME", "N", "EUR_CALL", "AMER_CALL", "EUR_PUT",
"AMER_PUT")
sigma = 0.01
a = 0.1
hwModel = FinModelRatesHW(sigma, a)
K = 102.0
vec_ec = []
vec_ac = []
vec_ep = []
vec_ap = []
num_stepsVector = range(100, 500, 100)
for num_steps in num_stepsVector:
hwModel = FinModelRatesHW(sigma, a, num_steps)
start = time.time()
europeanCallBondOption = BondOption(bond, expiry_date, K, face,
FinOptionTypes.EUROPEAN_CALL)
v_ec = europeanCallBondOption.value(settlement_date, discount_curve,
hwModel)
americanCallBondOption = BondOption(bond, expiry_date, K, face,
FinOptionTypes.AMERICAN_CALL)
v_ac = americanCallBondOption.value(settlement_date, discount_curve,
hwModel)
europeanPutBondOption = BondOption(bond, expiry_date, K, face,
FinOptionTypes.EUROPEAN_PUT)
v_ep = europeanPutBondOption.value(settlement_date, discount_curve,
hwModel)
americanPutBondOption = BondOption(bond, expiry_date, K, face,
FinOptionTypes.AMERICAN_PUT)
v_ap = americanPutBondOption.value(settlement_date, discount_curve,
hwModel)
end = time.time()
period = end - start
testCases.print(period, num_steps, v_ec, v_ac, v_ep, v_ap)
vec_ec.append(v_ec)
vec_ac.append(v_ac)
vec_ep.append(v_ep)
vec_ap.append(v_ap)
if plotGraphs:
plt.figure()
plt.plot(num_stepsVector, vec_ac, label="American Call")
plt.legend()
plt.figure()
plt.plot(num_stepsVector, vec_ap, label="American Put")
plt.legend()
def test_BondOptionEuropeanConvergence():
# CONVERGENCE TESTS
# COMPARE AMERICAN TREE VERSUS JAMSHIDIAN IN EUROPEAN LIMIT TO CHECK THAT
# TREE HAS BEEN CORRECTLY CONSTRUCTED. FIND VERY GOOD AGREEMENT.
# Build discount curve
settlement_date = Date(1, 12, 2019)
discount_curve = DiscountCurveFlat(settlement_date, 0.05,
FrequencyTypes.CONTINUOUS)
# Bond details
issue_date = Date(1, 12, 2015)
maturity_date = Date(1, 12, 2020)
coupon = 0.05
freq_type = FrequencyTypes.ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
# Option Details - put expiry in the middle of a coupon period
expiry_date = Date(1, 3, 2020)
strikePrice = 100.0
face = 100.0
timeSteps = range(100, 400, 100)
strikePrice = 100.0
testCases.header("TIME", "N", "PUT_JAM", "PUT_TREE", "CALL_JAM",
"CALL_TREE")
for numTimeSteps in timeSteps:
sigma = 0.05
a = 0.1
start = time.time()
optionType = FinOptionTypes.EUROPEAN_PUT
bondOption1 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
model1 = FinModelRatesHW(sigma, a, numTimeSteps)
v1put = bondOption1.value(settlement_date, discount_curve, model1)
bondOption2 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
model2 = FinModelRatesHW(sigma, a, numTimeSteps,
FinHWEuropeanCalcType.EXPIRY_ONLY)
v2put = bondOption2.value(settlement_date, discount_curve, model2)
optionType = FinOptionTypes.EUROPEAN_CALL
bondOption1 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
model1 = FinModelRatesHW(sigma, a, numTimeSteps)
v1call = bondOption1.value(settlement_date, discount_curve, model1)
bondOption2 = BondOption(bond, expiry_date, strikePrice, face,
optionType)
model2 = FinModelRatesHW(sigma, a, numTimeSteps,
FinHWEuropeanCalcType.EXPIRY_TREE)
v2call = bondOption2.value(settlement_date, discount_curve, model2)
end = time.time()
period = end - start
testCases.print(period, numTimeSteps, v1put, v2put, v1call, v2call)
def test_FinEquityLookBackOption():
valuation_date = Date(1, 1, 2015)
expiry_date = Date(1, 1, 2016)
stock_price = 100.0
volatility = 0.3
interestRate = 0.05
dividendYield = 0.01
num_pathsRange = [10000]
stock_priceRange = range(90, 110, 10)
num_steps_per_year = 252
discount_curve = DiscountCurveFlat(valuation_date, interestRate)
dividendCurve = DiscountCurveFlat(valuation_date, dividendYield)
###############################################################################
testCases.header(
"NUMPATHS",
"OPTION_TYPE",
"S",
"SMIN",
"VALUE",
"VALUE_MC",
"DIFF",
"TIME")
optionType = FinOptionTypes.EUROPEAN_CALL
for stock_price in stock_priceRange:
for num_paths in num_pathsRange:
option = FinEquityFloatLookbackOption(expiry_date, optionType)
stockMin = stock_price
value = option.value(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMin)
start = time.time()
valueMC = option.valueMC(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMin,
num_paths,
num_steps_per_year)
end = time.time()
timeElapsed = round(end - start, 3)
diff = valueMC - value
testCases.print(
num_paths,
optionType,
stock_price,
stockMin,
value,
valueMC,
diff,
timeElapsed)
testCases.header(
"NUMPATHS",
"OPTION_TYPE",
"S",
"SMIN",
"VALUE",
"VALUE_MC",
"DIFF",
"TIME")
optionType = FinOptionTypes.EUROPEAN_CALL
for stock_price in stock_priceRange:
for num_paths in num_pathsRange:
option = FinEquityFloatLookbackOption(expiry_date, optionType)
stockMin = stock_price - 10
value = option.value(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMin)
start = time.time()
valueMC = option.valueMC(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMin,
num_paths,
num_steps_per_year)
end = time.time()
timeElapsed = round(end - start, 3)
diff = valueMC - value
testCases.print(
num_paths,
optionType,
stock_price,
stockMin,
value,
valueMC,
diff,
timeElapsed)
testCases.header(
"NUMPATHS",
"OPTION_TYPE",
"S",
"SMAX",
"VALUE",
"VALUE_MC",
"DIFF",
"TIME")
optionType = FinOptionTypes.EUROPEAN_PUT
for stock_price in stock_priceRange:
for num_paths in num_pathsRange:
option = FinEquityFloatLookbackOption(expiry_date, optionType)
stockMax = stock_price
value = option.value(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMax)
start = time.time()
valueMC = option.valueMC(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMax,
num_paths,
num_steps_per_year)
end = time.time()
timeElapsed = round(end - start, 3)
diff = valueMC - value
testCases.print(
num_paths,
optionType,
stock_price,
stockMax,
value,
valueMC,
diff,
timeElapsed)
testCases.header(
"NUMPATHS",
"OPTION_TYPE",
"S",
"SMAX",
"VALUE",
"VALUE_MC",
"DIFF",
"TIME")
optionType = FinOptionTypes.EUROPEAN_PUT
for stock_price in stock_priceRange:
for num_paths in num_pathsRange:
option = FinEquityFloatLookbackOption(expiry_date, optionType)
stockMax = stock_price + 10
value = option.value(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMax)
start = time.time()
valueMC = option.valueMC(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMax,
num_paths,
num_steps_per_year)
end = time.time()
timeElapsed = round(end - start, 3)
diff = valueMC - value
testCases.print(
num_paths,
optionType,
stock_price,
stockMax,
value,
valueMC,
diff,
timeElapsed)
###############################################################################
###############################################################################
stock_priceRange = range(90, 110, 10)
num_steps_per_year = 252
testCases.header(
"NUMPATHS",
"OPTION_TYPE",
"S",
"K",
"SMAX",
"VALUE",
"VALUE_MC",
"DIFF",
"TIME")
optionType = FinOptionTypes.EUROPEAN_CALL
k = 95.0
for stock_price in stock_priceRange:
for num_paths in num_pathsRange:
option = FinEquityFixedLookbackOption(expiry_date, optionType, k)
stockMax = stock_price
value = option.value(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMax)
start = time.time()
valueMC = option.valueMC(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMax,
num_paths,
num_steps_per_year)
end = time.time()
timeElapsed = round(end - start, 3)
diff = valueMC - value
testCases.print(
num_paths,
optionType,
stock_price,
k,
stockMax,
value,
valueMC,
diff,
timeElapsed)
testCases.header(
"NUMPATHS",
"OPTION_TYPE",
"S",
"K",
"SMAX",
"VALUE",
"VALUE_MC",
"DIFF",
"TIME")
optionType = FinOptionTypes.EUROPEAN_CALL
k = 100.0
for stock_price in stock_priceRange:
for num_paths in num_pathsRange:
option = FinEquityFixedLookbackOption(expiry_date, optionType, k)
stockMax = stock_price
value = option.value(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMax)
start = time.time()
valueMC = option.valueMC(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMax,
num_paths,
num_steps_per_year)
end = time.time()
timeElapsed = round(end - start, 3)
diff = valueMC - value
testCases.print(
num_paths,
optionType,
stock_price,
k,
stockMax,
value,
valueMC,
diff,
timeElapsed)
testCases.header(
"NUMPATHS",
"OPTION_TYPE",
"S",
"K",
"SMAX",
"VALUE",
"VALUE_MC",
"DIFF",
"TIME")
optionType = FinOptionTypes.EUROPEAN_CALL
k = 105.0
for stock_price in stock_priceRange:
for num_paths in num_pathsRange:
option = FinEquityFixedLookbackOption(expiry_date, optionType, k)
stockMax = stock_price + 10.0
value = option.value(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMax)
start = time.time()
valueMC = option.valueMC(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMax,
num_paths,
num_steps_per_year)
end = time.time()
timeElapsed = round(end - start, 3)
diff = valueMC - value
testCases.print(
num_paths,
optionType,
stock_price,
k,
stockMax,
value,
valueMC,
diff,
timeElapsed)
testCases.header(
"NUMPATHS",
"OPTION_TYPE",
"S",
"K",
"SMIN",
"VALUE",
"VALUE_MC",
"DIFF",
"TIME")
optionType = FinOptionTypes.EUROPEAN_PUT
k = 95.0
for stock_price in stock_priceRange:
for num_paths in num_pathsRange:
option = FinEquityFixedLookbackOption(expiry_date, optionType, k)
stockMin = stock_price
value = option.value(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMin)
start = time.time()
valueMC = option.valueMC(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMin,
num_paths,
num_steps_per_year)
end = time.time()
timeElapsed = round(end - start, 3)
diff = valueMC - value
testCases.print(
num_paths,
optionType,
stock_price,
k,
stockMin,
value,
valueMC,
diff,
timeElapsed)
testCases.header(
"NUMPATHS",
"OPTION_TYPE",
"S",
"K",
"SMIN",
"VALUE",
"VALUE_MC",
"DIFF",
"TIME")
optionType = FinOptionTypes.EUROPEAN_PUT
k = 100.0
for stock_price in stock_priceRange:
for num_paths in num_pathsRange:
option = FinEquityFixedLookbackOption(expiry_date, optionType, k)
stockMin = stock_price
value = option.value(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMin)
start = time.time()
valueMC = option.valueMC(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMin,
num_paths,
num_steps_per_year)
end = time.time()
timeElapsed = round(end - start, 3)
diff = valueMC - value
testCases.print(
num_paths,
optionType,
stock_price,
k,
stockMin,
value,
valueMC,
diff,
timeElapsed)
testCases.header(
"NUMPATHS",
"OPTION_TYPE",
"S",
"K",
"SMIN",
"VALUE",
"VALUE_MC",
"DIFF",
"TIME")
optionType = FinOptionTypes.EUROPEAN_PUT
k = 105.0
for stock_price in stock_priceRange:
for num_paths in num_pathsRange:
option = FinEquityFixedLookbackOption(expiry_date, optionType, k)
stockMin = stock_price - 10.0
value = option.value(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMin)
start = time.time()
valueMC = option.valueMC(
valuation_date,
stock_price,
discount_curve,
dividendCurve,
volatility,
stockMin,
num_paths,
num_steps_per_year)
end = time.time()
timeElapsed = round(end - start, 3)
diff = valueMC - value
testCases.print(
num_paths,
optionType,
stock_price,
k,
stockMin,
value,
valueMC,
diff,
timeElapsed)