def testIborSwaptionModels():
##########################################################################
# COMPARISON OF MODELS
##########################################################################
valuation_date = Date(1, 1, 2011)
libor_curve = test_ibor_depositsAndSwaps(valuation_date)
exercise_date = Date(1, 1, 2012)
swapMaturityDate = Date(1, 1, 2017)
swapFixedFrequencyType = FrequencyTypes.SEMI_ANNUAL
swapFixedDayCountType = DayCountTypes.ACT_365F
strikes = np.linspace(0.02, 0.08, 5)
testCases.header("LAB", "STRIKE", "BLK", "BLK_SHFT", "SABR", "SABR_SHFT",
"HW", "BK")
model1 = Black(0.00001)
model2 = BlackShifted(0.00001, 0.0)
model3 = SABR(0.013, 0.5, 0.5, 0.5)
model4 = SABRShifted(0.013, 0.5, 0.5, 0.5, -0.008)
model5 = HWTree(0.00001, 0.00001)
model6 = BKTree(0.01, 0.01)
settlement_date = valuation_date.add_weekdays(2)
for k in strikes:
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date,
swapMaturityDate, swaptionType, k,
swapFixedFrequencyType, swapFixedDayCountType)
swap1 = swaption.value(valuation_date, libor_curve, model1)
swap2 = swaption.value(valuation_date, libor_curve, model2)
swap3 = swaption.value(valuation_date, libor_curve, model3)
swap4 = swaption.value(valuation_date, libor_curve, model4)
swap5 = swaption.value(valuation_date, libor_curve, model5)
swap6 = swaption.value(valuation_date, libor_curve, model6)
testCases.print("PAY", k, swap1, swap2, swap3, swap4, swap5, swap6)
testCases.header("LABEL", "STRIKE", "BLK", "BLK_SHFTD", "SABR",
"SABR_SHFTD", "HW", "BK")
for k in strikes:
swaptionType = SwapTypes.RECEIVE
swaption = IborSwaption(settlement_date, exercise_date,
swapMaturityDate, swaptionType, k,
swapFixedFrequencyType, swapFixedDayCountType)
swap1 = swaption.value(valuation_date, libor_curve, model1)
swap2 = swaption.value(valuation_date, libor_curve, model2)
swap3 = swaption.value(valuation_date, libor_curve, model3)
swap4 = swaption.value(valuation_date, libor_curve, model4)
swap5 = swaption.value(valuation_date, libor_curve, model5)
swap6 = swaption.value(valuation_date, libor_curve, model6)
testCases.print("REC", k, swap1, swap2, swap3, swap4, swap5, swap6)
def test_HullWhiteExampleOne():
# HULL BOOK INITIAL EXAMPLE SECTION 28.7 HW EDITION 6
times = [0.0, 0.5000, 1.00000, 1.50000, 2.00000, 2.500000, 3.00000]
zeros = [0.03, 0.0343, 0.03824, 0.04183, 0.04512, 0.048512, 0.05086]
times = np.array(times)
zeros = np.array(zeros)
dfs = np.exp(-zeros * times)
start_date = Date(1, 12, 2019)
end_date = Date(1, 12, 2022)
sigma = 0.01
a = 0.1
num_time_steps = 3
model = HWTree(sigma, a, num_time_steps)
treeMat = (end_date - start_date) / gDaysInYear
model.build_tree(treeMat, times, dfs)
def test_matlab_hw():
sigma = 0.01 # basis point volatility
a = 0.1
model = HWTree(sigma, a, num_time_steps)
v = puttableBond_matlab.value(settlement_date_matlab,
discount_curve_matlab, model)
assert round(v['bondwithoption'], 4) == 102.8733
assert round(v['bondpure'], 4) == 102.0603
def test_quantlib_hw():
# the value used in blog of 12% bp vol is unrealistic
sigma = 0.12 # basis point volatility
a = 0.03
model = HWTree(sigma, a, num_time_steps)
v = puttableBond_quantlib.value(settlement_date_quantlib,
discount_curve_quantlib, model)
assert round(v['bondwithoption'], 4) == 68.8665
assert round(v['bondpure'], 4) == 95.0619
def test_american_put_hw():
option_type = OptionTypes.AMERICAN_PUT
strike_price = 100
bond_option = BondOption(bond, expiry_date, strike_price, face,
option_type)
sigma = 0.02
a = 0.1
model = HWTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
assert round(v, 4) == 4.7948
def test_european_put_hw():
option_type = OptionTypes.EUROPEAN_PUT
strike_price = 100
bond_option = BondOption(bond, expiry_date, strike_price, face,
option_type)
sigma = 0.01
a = 0.1
model = HWTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
assert round(v, 4) == 2.2767
def test_hw_bermudan_exercise():
fixed_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
sigma = 0.000001
a = 0.01
model = HWTree(sigma, a, num_time_steps)
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
assert round(valuePay, 4) == 6353.3815
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
assert valueRec == 0.0
sigma = 0.01
a = 0.01
model = HWTree(sigma, a, num_time_steps)
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
assert round(valuePay, 4) == 16609.3646
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
assert round(valueRec, 4) == 10406.4558
def test_european_call_hw():
option_type = OptionTypes.EUROPEAN_CALL
strike_price = 100
num_time_steps = 100
bond_option = BondOption(bond, expiry_date, strike_price, face,
option_type)
sigma = 0.01
a = 0.1
model = HWTree(sigma, a, num_time_steps)
v = bond_option.value(settlement_date, discount_curve, model)
assert round(v, 4) == 1.8809
def test_FinIborCapFloor():
todayDate = Date(20, 6, 2019)
valuation_date = todayDate
start_date = todayDate.add_weekdays(2)
maturity_date = start_date.add_tenor("1Y")
libor_curve = test_ibor_depositsAndSwaps(todayDate)
# The capfloor has begun
# lastFixing = 0.028
##########################################################################
# COMPARISON OF MODELS
##########################################################################
strikes = np.linspace(0.02, 0.08, 5)
testCases.header("LABEL", "STRIKE", "BLK", "BLK_SHFTD", "SABR",
"SABR_SHFTD", "HW", "BACH")
model1 = Black(0.20)
model2 = BlackShifted(0.25, 0.0)
model3 = SABR(0.013, 0.5, 0.5, 0.5)
model4 = SABRShifted(0.013, 0.5, 0.5, 0.5, -0.008)
model5 = HWTree(0.30, 0.01)
model6 = Bachelier(0.01)
for k in strikes:
capFloorType = FinCapFloorTypes.CAP
capfloor = IborCapFloor(start_date, maturity_date, capFloorType, k)
cvalue1 = capfloor.value(valuation_date, libor_curve, model1)
cvalue2 = capfloor.value(valuation_date, libor_curve, model2)
cvalue3 = capfloor.value(valuation_date, libor_curve, model3)
cvalue4 = capfloor.value(valuation_date, libor_curve, model4)
cvalue5 = capfloor.value(valuation_date, libor_curve, model5)
cvalue6 = capfloor.value(valuation_date, libor_curve, model6)
testCases.print("CAP", k, cvalue1, cvalue2,
cvalue3, cvalue4, cvalue5, cvalue6)
testCases.header("LABEL", "STRIKE", "BLK", "BLK_SHFTD", "SABR",
"SABR_SHFTD", "HW", "BACH")
for k in strikes:
capFloorType = FinCapFloorTypes.FLOOR
capfloor = IborCapFloor(start_date, maturity_date, capFloorType, k)
fvalue1 = capfloor.value(valuation_date, libor_curve, model1)
fvalue2 = capfloor.value(valuation_date, libor_curve, model2)
fvalue3 = capfloor.value(valuation_date, libor_curve, model3)
fvalue4 = capfloor.value(valuation_date, libor_curve, model4)
fvalue5 = capfloor.value(valuation_date, libor_curve, model5)
fvalue6 = capfloor.value(valuation_date, libor_curve, model6)
testCases.print("FLR", k, fvalue1, fvalue2,
fvalue3, fvalue4, fvalue5, fvalue6)
###############################################################################
# PUT CALL CHECK
###############################################################################
testCases.header("LABEL", "STRIKE", "BLK", "BLK_SHFTD", "SABR",
"SABR SHFTD", "HW", "BACH")
for k in strikes:
capFloorType = FinCapFloorTypes.CAP
capfloor = IborCapFloor(start_date, maturity_date, capFloorType, k)
cvalue1 = capfloor.value(valuation_date, libor_curve, model1)
cvalue2 = capfloor.value(valuation_date, libor_curve, model2)
cvalue3 = capfloor.value(valuation_date, libor_curve, model3)
cvalue4 = capfloor.value(valuation_date, libor_curve, model4)
cvalue5 = capfloor.value(valuation_date, libor_curve, model5)
cvalue6 = capfloor.value(valuation_date, libor_curve, model6)
capFloorType = FinCapFloorTypes.FLOOR
capfloor = IborCapFloor(start_date, maturity_date, capFloorType, k)
fvalue1 = capfloor.value(valuation_date, libor_curve, model1)
fvalue2 = capfloor.value(valuation_date, libor_curve, model2)
fvalue3 = capfloor.value(valuation_date, libor_curve, model3)
fvalue4 = capfloor.value(valuation_date, libor_curve, model4)
fvalue5 = capfloor.value(valuation_date, libor_curve, model5)
fvalue6 = capfloor.value(valuation_date, libor_curve, model6)
pcvalue1 = cvalue1 - fvalue1
pcvalue2 = cvalue2 - fvalue2
pcvalue3 = cvalue3 - fvalue3
pcvalue4 = cvalue4 - fvalue4
pcvalue5 = cvalue5 - fvalue5
pcvalue6 = cvalue6 - fvalue6
testCases.print("PUT_CALL", k, pcvalue1, pcvalue2, pcvalue3,
pcvalue4, pcvalue5, pcvalue6)
def test_BondOptionDerivaGem():
# See https://github.com/domokane/FinancePy/issues/98
settlement_date = Date(1, 12, 2019)
rate = 0.05
dcType = DayCountTypes.THIRTY_360_BOND
fixedFreq = FrequencyTypes.SEMI_ANNUAL
discount_curve = DiscountCurveFlat(settlement_date, rate, fixedFreq,
dcType)
issue_date = Date(1, 12, 2018)
expiry_date = settlement_date.add_tenor("18m")
maturity_date = settlement_date.add_tenor("10Y")
coupon = 0.05
freqType = FrequencyTypes.SEMI_ANNUAL
accrualType = DayCountTypes.THIRTY_360_BOND
bond = Bond(issue_date, maturity_date, coupon, freqType, accrualType)
strike_price = 100.0
face = 100.0
europeanCallBondOption = BondOption(bond, expiry_date, strike_price, face,
OptionTypes.EUROPEAN_CALL)
cp = bond.clean_price_from_discount_curve(expiry_date, discount_curve)
fp = bond.full_price_from_discount_curve(expiry_date, discount_curve)
# print("Fixed Income Clean Price: %9.3f"% cp)
# print("Fixed Income Full Price: %9.3f"% fp)
num_steps = 500
sigma = 0.0125
a = 0.1
modelHW = HWTree(sigma, a, num_steps)
ec = europeanCallBondOption.value(settlement_date, discount_curve, modelHW)
###########################################################################
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
numFlows = len(bond._flow_dates)
for i in range(0, numFlows):
pcd = bond._flow_dates[i - 1]
ncd = bond._flow_dates[i]
if ncd > settlement_date:
if len(couponTimes) == 0:
flowTime = (pcd - settlement_date) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
flowTime = (ncd - settlement_date) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
y = 0.05
times = np.linspace(0, 10, 21)
dfs = np.power(1 + y / 2, -times * 2)
sigma = 0.0125
a = 0.1
model = HWTree(sigma, a, None)
# Test convergence
texp = (expiry_date - settlement_date) / gDaysInYear
tmat = (maturity_date - settlement_date) / gDaysInYear
# Jamshidian approach
vjam = model.european_bond_option_jamshidian(texp, strike_price, face,
couponTimes, couponFlows,
times, dfs)
# print("Jamshidian:", vjam)
model._num_time_steps = 100
model.build_tree(tmat, times, dfs)
exerciseType = FinExerciseTypes.EUROPEAN
vHW = model.bond_option(texp, strike_price, face, couponTimes, couponFlows,
exerciseType)
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._accrued_interest)
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")
num_time_steps = range(100, 1000, 100)
strike_prices = [90, 100, 110, 120]
for strike_price in strike_prices:
callIntrinsic = max(spotCleanValue - strike_price, 0)
putIntrinsic = max(strike_price - spotCleanValue, 0)
callIntrinsicPV = max(fwdCleanValue - strike_price, 0) * dfExpiry
putIntrinsicPV = max(strike_price - fwdCleanValue, 0) * dfExpiry
for num_steps in num_time_steps:
sigma = 0.0000001
a = 0.1
model = HWTree(sigma, a, num_steps)
option_type = OptionTypes.EUROPEAN_CALL
bond_option1 = BondOption(bond, expiry_date, strike_price, face,
option_type)
v1 = bond_option1.value(settlement_date, discount_curve, model)
option_type = OptionTypes.AMERICAN_CALL
bond_option2 = BondOption(bond, expiry_date, strike_price, face,
option_type)
v2 = bond_option2.value(settlement_date, discount_curve, model)
option_type = OptionTypes.EUROPEAN_PUT
bond_option3 = BondOption(bond, expiry_date, strike_price, face,
option_type)
v3 = bond_option3.value(settlement_date, discount_curve, model)
option_type = OptionTypes.AMERICAN_PUT
bond_option4 = BondOption(bond, expiry_date, strike_price, face,
option_type)
v4 = bond_option4.value(settlement_date, discount_curve, model)
testCases.print(strike_price, num_steps, callIntrinsic,
callIntrinsicPV, v1, v2, putIntrinsic,
putIntrinsicPV, v3, v4)
def test_BondOption():
settlement_date = Date(1, 12, 2019)
issue_date = Date(1, 12, 2018)
maturity_date = settlement_date.add_tenor("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)
times = np.linspace(0, 10.0, 21)
dfs = np.exp(-0.05 * times)
dates = settlement_date.add_years(times)
discount_curve = DiscountCurve(settlement_date, dates, dfs)
expiry_date = settlement_date.add_tenor("18m")
strike_price = 105.0
face = 100.0
###########################################################################
strikes = [80, 85, 90, 95, 100, 105, 110, 115, 120]
option_type = OptionTypes.EUROPEAN_CALL
testCases.header("LABEL", "VALUE")
price = bond.clean_price_from_discount_curve(settlement_date,
discount_curve)
testCases.print("Fixed Income Price:", price)
num_time_steps = 100
testCases.banner("HW EUROPEAN CALL")
testCases.header("STRIKE", "VALUE")
for strike_price in strikes:
sigma = 0.01
a = 0.1
bond_option = BondOption(bond, expiry_date, strike_price, face,
option_type)
model = HWTree(sigma, a, num_time_steps)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print(strike_price, v)
###########################################################################
option_type = OptionTypes.AMERICAN_CALL
price = bond.clean_price_from_discount_curve(settlement_date,
discount_curve)
testCases.header("LABEL", "VALUE")
testCases.print("Fixed Income Price:", price)
testCases.banner("HW AMERICAN CALL")
testCases.header("STRIKE", "VALUE")
for strike_price in strikes:
sigma = 0.01
a = 0.1
bond_option = BondOption(bond, expiry_date, strike_price, face,
option_type)
model = HWTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print(strike_price, v)
###########################################################################
option_type = OptionTypes.EUROPEAN_PUT
testCases.banner("HW EUROPEAN PUT")
testCases.header("STRIKE", "VALUE")
price = bond.clean_price_from_discount_curve(settlement_date,
discount_curve)
for strike_price in strikes:
sigma = 0.01
a = 0.1
bond_option = BondOption(bond, expiry_date, strike_price, face,
option_type)
model = HWTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print(strike_price, v)
###########################################################################
option_type = OptionTypes.AMERICAN_PUT
testCases.banner("HW AMERICAN PUT")
testCases.header("STRIKE", "VALUE")
price = bond.clean_price_from_discount_curve(settlement_date,
discount_curve)
for strike_price in strikes:
sigma = 0.02
a = 0.1
bond_option = BondOption(bond, expiry_date, strike_price, face,
option_type)
model = HWTree(sigma, a)
v = bond_option.value(settlement_date, discount_curve, model)
testCases.print(strike_price, v)
return libor_curve
valuation_date = Date(1, 1, 2011)
exercise_date = Date(1, 1, 2012)
swapMaturityDate = Date(1, 1, 2017)
swapFixedFrequencyType = FrequencyTypes.SEMI_ANNUAL
swapFixedDayCountType = DayCountTypes.ACT_365F
model1 = Black(0.00001)
model2 = BlackShifted(0.00001, 0.0)
model3 = SABR(0.013, 0.5, 0.5, 0.5)
model4 = SABRShifted(0.013, 0.5, 0.5, 0.5, -0.008)
model5 = HWTree(0.00001, 0.00001)
model6 = BKTree(0.01, 0.01)
settlement_date = valuation_date.add_weekdays(2)
libor_curve = build_curve(valuation_date)
def test_pay():
libor_curve = build_curve(valuation_date)
swaptionType = SwapTypes.PAY
k = 0.02
swaption = IborSwaption(settlement_date, exercise_date, swapMaturityDate,
swaptionType, k, swapFixedFrequencyType,
swapFixedDayCountType)
def test_HullWhiteCallableBond():
# Valuation of a European option on a coupon bearing bond
settlement_date = Date(1, 12, 2019)
issue_date = Date(1, 12, 2018)
maturity_date = settlement_date.add_tenor("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)
coupon_times = []
coupon_flows = []
cpn = bond._coupon / bond._frequency
for flow_date in bond._coupon_dates[1:]:
if flow_date > settlement_date:
flow_time = (flow_date - settlement_date) / gDaysInYear
coupon_times.append(flow_time)
coupon_flows.append(cpn)
coupon_times = np.array(coupon_times)
coupon_flows = np.array(coupon_flows)
###########################################################################
# Set up the call and put times and prices
###########################################################################
call_dates = []
call_prices = []
callPx = 120.0
call_dates.append(settlement_date.add_tenor("2Y"))
call_prices.append(callPx)
call_dates.append(settlement_date.add_tenor("3Y"))
call_prices.append(callPx)
call_dates.append(settlement_date.add_tenor("4Y"))
call_prices.append(callPx)
call_dates.append(settlement_date.add_tenor("5Y"))
call_prices.append(callPx)
call_dates.append(settlement_date.add_tenor("6Y"))
call_prices.append(callPx)
call_dates.append(settlement_date.add_tenor("7Y"))
call_prices.append(callPx)
call_dates.append(settlement_date.add_tenor("8Y"))
call_prices.append(callPx)
call_times = []
for dt in call_dates:
t = (dt - settlement_date) / gDaysInYear
call_times.append(t)
put_dates = []
put_prices = []
putPx = 98.0
put_dates.append(settlement_date.add_tenor("2Y"))
put_prices.append(putPx)
put_dates.append(settlement_date.add_tenor("3Y"))
put_prices.append(putPx)
put_dates.append(settlement_date.add_tenor("4Y"))
put_prices.append(putPx)
put_dates.append(settlement_date.add_tenor("5Y"))
put_prices.append(putPx)
put_dates.append(settlement_date.add_tenor("6Y"))
put_prices.append(putPx)
put_dates.append(settlement_date.add_tenor("7Y"))
put_prices.append(putPx)
put_dates.append(settlement_date.add_tenor("8Y"))
put_prices.append(putPx)
put_times = []
for dt in put_dates:
t = (dt - settlement_date) / gDaysInYear
put_times.append(t)
###########################################################################
tmat = (maturity_date - settlement_date) / gDaysInYear
curve = DiscountCurveFlat(settlement_date, 0.05, FrequencyTypes.CONTINUOUS)
dfs = []
times = []
for dt in bond._coupon_dates:
if dt > settlement_date:
t = (dt - settlement_date) / gDaysInYear
df = curve.df(dt)
times.append(t)
dfs.append(df)
dfs = np.array(dfs)
times = np.array(times)
###########################################################################
v1 = bond.clean_price_from_discount_curve(settlement_date, curve)
sigma = 0.02 # basis point volatility
a = 0.01
# Test convergence
num_steps_list = [100, 200, 500, 1000]
tmat = (maturity_date - settlement_date) / gDaysInYear
testCases.header("NUMSTEPS", "TIME", "BOND_ONLY", "CALLABLE_BOND")
for num_time_steps in num_steps_list:
start = time.time()
model = HWTree(sigma, a, num_time_steps)
model.build_tree(tmat, times, dfs)
v2 = model.callable_puttable_bond_tree(coupon_times, coupon_flows,
call_times, call_prices,
put_times, put_prices, 100.0)
end = time.time()
period = end - start
testCases.print(num_time_steps, period, v1, v2)
def test_BondEmbeddedOptionMATLAB():
# https://fr.mathworks.com/help/fininst/optembndbyhw.html
# I FIND THAT THE PRICE CONVERGES TO 102.88 WHICH IS CLOSE TO 102.9127
# FOUND BY MATLAB ALTHOUGH THEY DO NOT EXAMINE THE ASYMPTOTIC PRICE
# WHICH MIGHT BE A BETTER MATCH
settlement_date = Date(1, 1, 2007)
valuation_date = settlement_date
###########################################################################
dcType = DayCountTypes.THIRTY_E_360
fixedFreq = FrequencyTypes.ANNUAL
fixed_leg_type = SwapTypes.PAY
swap1 = IborSwap(settlement_date, "1Y", fixed_leg_type, 0.0350, fixedFreq,
dcType)
swap2 = IborSwap(settlement_date, "2Y", fixed_leg_type, 0.0400, fixedFreq,
dcType)
swap3 = IborSwap(settlement_date, "3Y", fixed_leg_type, 0.0450, fixedFreq,
dcType)
swaps = [swap1, swap2, swap3]
discount_curve = IborSingleCurve(valuation_date, [], [], swaps)
###########################################################################
issue_date = Date(1, 1, 2004)
maturity_date = Date(1, 1, 2010)
coupon = 0.0525
freq_type = FrequencyTypes.ANNUAL
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
call_dates = []
call_prices = []
put_dates = []
put_prices = []
putDate = Date(1, 1, 2008)
for _ in range(0, 24):
put_dates.append(putDate)
put_prices.append(100)
putDate = putDate.add_months(1)
testCases.header("BOND PRICE", "PRICE")
v = bond.clean_price_from_discount_curve(settlement_date, discount_curve)
testCases.print("Bond Pure Price:", v)
sigma = 0.01 # basis point volatility
a = 0.1
puttableBond = BondEmbeddedOption(issue_date, maturity_date, coupon,
freq_type, accrual_type, call_dates,
call_prices, put_dates, put_prices)
testCases.header("TIME", "NumTimeSteps", "BondWithOption", "BondPure")
timeSteps = range(50, 1000, 50)
values = []
for num_time_steps in timeSteps:
model = HWTree(sigma, a, num_time_steps)
start = time.time()
v = puttableBond.value(settlement_date, discount_curve, model)
end = time.time()
period = end - start
testCases.print(period, num_time_steps, v['bondwithoption'],
v['bondpure'])
values.append(v['bondwithoption'])
if plotGraphs:
plt.figure()
plt.plot(timeSteps, values)
def test_BondEmbeddedOptionQUANTLIB():
# Based on example at the nice blog on Quantlib at
# http://gouthamanbalaraman.com/blog/callable-bond-quantlib-python.html
# I get a price of 68.97 for 1000 time steps which is higher than the
# 68.38 found in blog article. But this is for 40 grid points.
# Note also that a basis point vol of 0.120 is 12% which is VERY HIGH!
valuation_date = Date(16, 8, 2016)
settlement_date = valuation_date.add_weekdays(3)
###########################################################################
discount_curve = DiscountCurveFlat(valuation_date, 0.035,
FrequencyTypes.SEMI_ANNUAL)
###########################################################################
issue_date = Date(15, 9, 2010)
maturity_date = Date(15, 9, 2022)
coupon = 0.025
freq_type = FrequencyTypes.QUARTERLY
accrual_type = DayCountTypes.ACT_ACT_ICMA
bond = Bond(issue_date, maturity_date, coupon, freq_type, accrual_type)
###########################################################################
# Set up the call and put times and prices
###########################################################################
nextCallDate = Date(15, 9, 2016)
call_dates = [nextCallDate]
call_prices = [100.0]
for _ in range(1, 24):
nextCallDate = nextCallDate.add_months(3)
call_dates.append(nextCallDate)
call_prices.append(100.0)
put_dates = []
put_prices = []
# the value used in blog of 12% bp vol is unrealistic
sigma = 0.12 # basis point volatility
a = 0.03
puttableBond = BondEmbeddedOption(issue_date, maturity_date, coupon,
freq_type, accrual_type, call_dates,
call_prices, put_dates, put_prices)
testCases.header("BOND PRICE", "PRICE")
v = bond.clean_price_from_discount_curve(settlement_date, discount_curve)
testCases.print("Bond Pure Price:", v)
testCases.header("TIME", "NumTimeSteps", "BondWithOption", "BondPure")
timeSteps = range(100, 200, 50)
values = []
for num_time_steps in timeSteps:
model = HWTree(sigma, a, num_time_steps)
start = time.time()
v = puttableBond.value(settlement_date, discount_curve, model)
end = time.time()
period = end - start
testCases.print(period, num_time_steps, v['bondwithoption'],
v['bondpure'])
values.append(v['bondwithoption'])
if plotGraphs:
plt.figure()
plt.title("Puttable Bond Price Convergence")
plt.plot(timeSteps, values)
def test_IborBermudanSwaptionBKModel():
""" 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
exercise_date = settlement_date.add_years(1)
swapMaturityDate = settlement_date.add_years(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 = IborSwap(exercise_date, swapMaturityDate, SwapTypes.PAY,
swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fwdSwapValue = fwdPAYSwap.value(settlement_date, libor_curve, libor_curve)
testCases.header("LABEL", "VALUE")
testCases.print("FWD SWAP VALUE", fwdSwapValue)
# fwdPAYSwap.print_fixed_leg_pv()
# Now we create the European swaptions
fixed_leg_type = SwapTypes.PAY
europeanSwaptionPay = IborSwaption(settlement_date, exercise_date,
swapMaturityDate, fixed_leg_type,
swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
europeanSwaptionRec = IborSwaption(settlement_date, exercise_date,
swapMaturityDate, fixed_leg_type,
swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
###########################################################################
###########################################################################
###########################################################################
# BLACK'S MODEL
###########################################################################
###########################################################################
###########################################################################
testCases.banner("======= ZERO VOLATILITY ========")
model = Black(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 = Black(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
num_time_steps = 100
model = BKTree(sigma, a, num_time_steps)
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 = BKTree(sigma, a, num_time_steps)
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_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.EUROPEAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
exercise_type = FinExerciseTypes.EUROPEAN
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, 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 = BKTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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 = BKTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, 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 = BKTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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 = BKTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BK PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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
num_time_steps = 200
model = BDTTree(sigma, num_time_steps)
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 = BDTTree(sigma, num_time_steps)
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_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.EUROPEAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= 0% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE BDT MODEL ========"
)
# Used BK with constant short-rate volatility
sigma = 0.000001
model = BDTTree(sigma, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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 = BDTTree(sigma, num_time_steps)
testCases.banner("BDT MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, 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 = BDTTree(sigma, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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 = BDTTree(sigma, num_time_steps)
# print("BDT MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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
num_time_steps = 200
model = HWTree(sigma, a, num_time_steps)
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 = HWTree(sigma, a, num_time_steps)
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_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.EUROPEAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
testCases.banner(
"======= 0% VOLATILITY BERMUDAN SWAPTION EUROPEAN EXERCISE HW MODEL ========"
)
sigma = 0.000001
model = HWTree(sigma, a, num_time_steps)
testCases.banner("BK MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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 = HWTree(sigma, a, num_time_steps)
testCases.banner("BDT MODEL BERMUDAN SWAPTION CLASS EUROPEAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN BDT PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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_leg_type = SwapTypes.PAY
exercise_type = FinExerciseTypes.BERMUDAN
bermudan_swaption_pay = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, swapFixedCoupon, swapFixedFrequencyType,
swapFixedDayCountType)
fixed_leg_type = SwapTypes.RECEIVE
bermudan_swaption_rec = IborBermudanSwaption(
settlement_date, exercise_date, swapMaturityDate, fixed_leg_type,
exercise_type, 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 = HWTree(sigma, a, num_time_steps)
testCases.banner("HW MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.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 = HWTree(sigma, a, num_time_steps)
testCases.banner("HW MODEL BERMUDAN SWAPTION CLASS BERMUDAN EXERCISE")
valuePay = bermudan_swaption_pay.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW PAY VALUE:", valuePay)
valueRec = bermudan_swaption_rec.value(valuation_date, libor_curve, model)
testCases.print("BERMUDAN HW REC VALUE:", valueRec)
payRec = valuePay - valueRec
testCases.print("PAY MINUS RECEIVER :", payRec)
def test_HullWhiteExampleTwo():
# HULL BOOK ZERO COUPON BOND EXAMPLE 28.1 SEE TABLE 28.3
# Replication may not be exact as I am using dates rather than times
zeroDays = [
0, 3, 31, 62, 94, 185, 367, 731, 1096, 1461, 1826, 2194, 2558, 2922,
3287, 3653
]
zero_rates = [
5.0, 5.01772, 4.98282, 4.97234, 4.96157, 4.99058, 5.09389, 5.79733,
6.30595, 6.73464, 6.94816, 7.08807, 7.27527, 7.30852, 7.39790, 7.49015
]
times = np.array(zeroDays) / 365.0
zeros = np.array(zero_rates) / 100.0
dfs = np.exp(-zeros * times)
start_date = Date(1, 12, 2019)
sigma = 0.01
a = 0.1
strike = 63.0
face = 100.0
expiry_date = start_date.add_tenor("3Y")
maturity_date = start_date.add_tenor("9Y")
texp = (expiry_date - start_date) / gDaysInYear
tmat = (maturity_date - start_date) / gDaysInYear
num_time_steps = None
model = HWTree(sigma, a, num_time_steps)
vAnal = model.option_on_zcb(texp, tmat, strike, face, times, dfs)
# Test convergence
num_steps_list = range(100, 500, 100)
analVector = []
treeVector = []
testCases.banner("Comparing option on zero coupon bond analytical vs Tree")
testCases.header("NUMTIMESTEP", "TIME", "VTREE_CALL", "VTREE_PUT",
"VANAL CALL", "VANAL_PUT", "CALLDIFF", "PUTDIFF")
for num_time_steps in num_steps_list:
start = time.time()
model = HWTree(sigma, a, num_time_steps)
model.build_tree(texp, times, dfs)
vTree1 = model.option_on_zero_coupon_bond_tree(texp, tmat, strike,
face)
model = HWTree(sigma, a, num_time_steps + 1)
model.build_tree(texp, times, dfs)
vTree2 = model.option_on_zero_coupon_bond_tree(texp, tmat, strike,
face)
end = time.time()
period = end - start
treeVector.append(vTree1['put'])
analVector.append(vAnal['put'])
vTreeCall = (vTree1['call'] + vTree2['call']) / 2.0
vTreePut = (vTree1['put'] + vTree2['put']) / 2.0
diffC = vTreeCall - vAnal['call']
diffP = vTreePut - vAnal['put']
testCases.print(num_time_steps, period, vTreeCall, vAnal['call'],
vTreePut, vAnal['put'], diffC, diffP)
def test_HullWhiteBondOption():
# Valuation of a European option on a coupon bearing bond
settlement_date = Date(1, 12, 2019)
issue_date = Date(1, 12, 2018)
expiry_date = settlement_date.add_tenor("18m")
maturity_date = settlement_date.add_tenor("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)
coupon_times = []
coupon_flows = []
cpn = bond._coupon / bond._frequency
num_flows = len(bond._coupon_dates)
for i in range(1, num_flows):
pcd = bond._coupon_dates[i - 1]
ncd = bond._coupon_dates[i]
if ncd > settlement_date:
if len(coupon_times) == 0:
flow_time = (pcd - settlement_date) / gDaysInYear
coupon_times.append(flow_time)
coupon_flows.append(cpn)
flow_time = (ncd - settlement_date) / gDaysInYear
coupon_times.append(flow_time)
coupon_flows.append(cpn)
coupon_times = np.array(coupon_times)
coupon_flows = np.array(coupon_flows)
strike_price = 100.0
face = 100.0
y = 0.05
times = np.linspace(0, 10, 21)
dfs = np.power(1 + y / 2, -times * 2)
sigma = 0.0000001
a = 0.1
model = HWTree(sigma, a, None)
# Test convergence
num_steps_list = range(50, 500, 50)
texp = (expiry_date - settlement_date) / gDaysInYear
vJam = model.european_bond_option_jamshidian(texp, strike_price, face,
coupon_times, coupon_flows,
times, dfs)
testCases.banner(
"Pricing bond option on tree that goes to bond maturity and one using european bond option tree that goes to expiry."
)
testCases.header("NUMSTEPS", "TIME", "EXPIRY_ONLY", "EXPIRY_TREE",
"JAMSHIDIAN")
for num_time_steps in num_steps_list:
start = time.time()
model = HWTree(sigma, a, num_time_steps,
FinHWEuropeanCalcType.EXPIRY_ONLY)
model.build_tree(texp, times, dfs)
exercise_type = FinExerciseTypes.EUROPEAN
v1 = model.bond_option(texp, strike_price, face, coupon_times,
coupon_flows, exercise_type)
model = HWTree(sigma, a, num_time_steps,
FinHWEuropeanCalcType.EXPIRY_TREE)
model.build_tree(texp, times, dfs)
v2 = model.bond_option(texp, strike_price, face, coupon_times,
coupon_flows, exercise_type)
end = time.time()
period = end - start
testCases.print(num_time_steps, period, v1, v2, vJam)
# plt.plot(num_steps_list, treeVector)
if 1 == 0:
print("RT")
print_tree(model._rt, 5)
print("BOND")
print_tree(model._bond_values, 5)
print("OPTION")
print_tree(model._option_values, 5)
def testIborSwaptionMatlabExamples():
# We value a European swaption using Black's model and try to replicate a
# ML example at https://fr.mathworks.com/help/fininst/swaptionbyblk.html
testCases.header("=======================================")
testCases.header("MATLAB EXAMPLE WITH FLAT TERM STRUCTURE")
testCases.header("=======================================")
valuation_date = Date(1, 1, 2010)
libor_curve = DiscountCurveFlat(valuation_date, 0.06,
FrequencyTypes.CONTINUOUS,
DayCountTypes.THIRTY_E_360)
settlement_date = Date(1, 1, 2011)
exercise_date = Date(1, 1, 2016)
maturity_date = Date(1, 1, 2019)
fixed_coupon = 0.062
fixed_frequency_type = FrequencyTypes.SEMI_ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
notional = 100.0
# Pricing a PAY
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional)
model = Black(0.20)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 2.071
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
###############################################################################
testCases.header("===================================")
testCases.header("MATLAB EXAMPLE WITH TERM STRUCTURE")
testCases.header("===================================")
valuation_date = Date(1, 1, 2010)
dates = [
Date(1, 1, 2011),
Date(1, 1, 2012),
Date(1, 1, 2013),
Date(1, 1, 2014),
Date(1, 1, 2015)
]
zero_rates = [0.03, 0.034, 0.037, 0.039, 0.040]
contFreq = FrequencyTypes.CONTINUOUS
interp_type = InterpTypes.LINEAR_ZERO_RATES
day_count_type = DayCountTypes.THIRTY_E_360
libor_curve = DiscountCurveZeros(valuation_date, dates, zero_rates,
contFreq, day_count_type, interp_type)
settlement_date = Date(1, 1, 2011)
exercise_date = Date(1, 1, 2012)
maturity_date = Date(1, 1, 2017)
fixed_coupon = 0.03
fixed_frequency_type = FrequencyTypes.SEMI_ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360
float_frequency_type = FrequencyTypes.SEMI_ANNUAL
float_day_count_type = DayCountTypes.THIRTY_E_360
notional = 1000.0
# Pricing a put
swaptionType = SwapTypes.RECEIVE
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional,
float_frequency_type, float_day_count_type)
model = Black(0.21)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 0.5771
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
###############################################################################
testCases.header("===================================")
testCases.header("MATLAB EXAMPLE WITH SHIFTED BLACK")
testCases.header("===================================")
valuation_date = Date(1, 1, 2016)
dates = [
Date(1, 1, 2017),
Date(1, 1, 2018),
Date(1, 1, 2019),
Date(1, 1, 2020),
Date(1, 1, 2021)
]
zero_rates = np.array([-0.02, 0.024, 0.047, 0.090, 0.12]) / 100.0
contFreq = FrequencyTypes.ANNUAL
interp_type = InterpTypes.LINEAR_ZERO_RATES
day_count_type = DayCountTypes.THIRTY_E_360
libor_curve = DiscountCurveZeros(valuation_date, dates, zero_rates,
contFreq, day_count_type, interp_type)
settlement_date = Date(1, 1, 2016)
exercise_date = Date(1, 1, 2017)
maturity_date = Date(1, 1, 2020)
fixed_coupon = -0.003
fixed_frequency_type = FrequencyTypes.SEMI_ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
float_frequency_type = FrequencyTypes.SEMI_ANNUAL
float_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
notional = 1000.0
# Pricing a PAY
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional,
float_frequency_type, float_day_count_type)
model = BlackShifted(0.31, 0.008)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 12.8301
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
###############################################################################
testCases.header("===================================")
testCases.header("MATLAB EXAMPLE WITH HULL WHITE")
testCases.header("===================================")
# https://fr.mathworks.com/help/fininst/swaptionbyhw.html
valuation_date = Date(1, 1, 2007)
dates = [
Date(1, 1, 2007),
Date(1, 7, 2007),
Date(1, 1, 2008),
Date(1, 7, 2008),
Date(1, 1, 2009),
Date(1, 7, 2009),
Date(1, 1, 2010),
Date(1, 7, 2010),
Date(1, 1, 2011),
Date(1, 7, 2011),
Date(1, 1, 2012)
]
zero_rates = np.array([0.075] * 11)
interp_type = InterpTypes.FLAT_FWD_RATES
day_count_type = DayCountTypes.THIRTY_E_360_ISDA
contFreq = FrequencyTypes.SEMI_ANNUAL
libor_curve = DiscountCurveZeros(valuation_date, dates, zero_rates,
contFreq, day_count_type, interp_type)
settlement_date = valuation_date
exercise_date = Date(1, 1, 2010)
maturity_date = Date(1, 1, 2012)
fixed_coupon = 0.04
fixed_frequency_type = FrequencyTypes.SEMI_ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
notional = 100.0
swaptionType = SwapTypes.RECEIVE
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional)
model = HWTree(0.05, 0.01)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 2.9201
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
###############################################################################
testCases.header("====================================")
testCases.header("MATLAB EXAMPLE WITH BLACK KARASINSKI")
testCases.header("====================================")
# https://fr.mathworks.com/help/fininst/swaptionbybk.html
valuation_date = Date(1, 1, 2007)
dates = [
Date(1, 1, 2007),
Date(1, 7, 2007),
Date(1, 1, 2008),
Date(1, 7, 2008),
Date(1, 1, 2009),
Date(1, 7, 2009),
Date(1, 1, 2010),
Date(1, 7, 2010),
Date(1, 1, 2011),
Date(1, 7, 2011),
Date(1, 1, 2012)
]
zero_rates = np.array([0.07] * 11)
interp_type = InterpTypes.FLAT_FWD_RATES
day_count_type = DayCountTypes.THIRTY_E_360_ISDA
contFreq = FrequencyTypes.SEMI_ANNUAL
libor_curve = DiscountCurveZeros(valuation_date, dates, zero_rates,
contFreq, day_count_type, interp_type)
settlement_date = valuation_date
exercise_date = Date(1, 1, 2011)
maturity_date = Date(1, 1, 2012)
fixed_frequency_type = FrequencyTypes.SEMI_ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
notional = 100.0
model = BKTree(0.1, 0.05, 200)
fixed_coupon = 0.07
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 0.3634
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
fixed_coupon = 0.0725
swaptionType = SwapTypes.RECEIVE
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 0.4798
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
###############################################################################
testCases.header("====================================")
testCases.header("MATLAB EXAMPLE WITH BLACK-DERMAN-TOY")
testCases.header("====================================")
# https://fr.mathworks.com/help/fininst/swaptionbybdt.html
valuation_date = Date(1, 1, 2007)
dates = [
Date(1, 1, 2007),
Date(1, 7, 2007),
Date(1, 1, 2008),
Date(1, 7, 2008),
Date(1, 1, 2009),
Date(1, 7, 2009),
Date(1, 1, 2010),
Date(1, 7, 2010),
Date(1, 1, 2011),
Date(1, 7, 2011),
Date(1, 1, 2012)
]
zero_rates = np.array([0.06] * 11)
interp_type = InterpTypes.FLAT_FWD_RATES
day_count_type = DayCountTypes.THIRTY_E_360_ISDA
contFreq = FrequencyTypes.ANNUAL
libor_curve = DiscountCurveZeros(valuation_date, dates, zero_rates,
contFreq, day_count_type, interp_type)
settlement_date = valuation_date
exercise_date = Date(1, 1, 2012)
maturity_date = Date(1, 1, 2015)
fixed_frequency_type = FrequencyTypes.ANNUAL
fixed_day_count_type = DayCountTypes.THIRTY_E_360_ISDA
notional = 100.0
fixed_coupon = 0.062
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date, maturity_date,
swaptionType, fixed_coupon, fixed_frequency_type,
fixed_day_count_type, notional)
model = BDTTree(0.20, 200)
v_finpy = swaption.value(valuation_date, libor_curve, model)
v_matlab = 2.0592
testCases.header("LABEL", "VALUE")
testCases.print("FP Price:", v_finpy)
testCases.print("MATLAB Prix:", v_matlab)
testCases.print("DIFF:", v_finpy - v_matlab)
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)
strike_price = 100.0
face = 100.0
timeSteps = range(100, 400, 100)
strike_price = 100.0
testCases.header("TIME", "N", "PUT_JAM", "PUT_TREE", "CALL_JAM",
"CALL_TREE")
for num_time_steps in timeSteps:
sigma = 0.05
a = 0.1
start = time.time()
option_type = OptionTypes.EUROPEAN_PUT
bond_option1 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model1 = HWTree(sigma, a, num_time_steps)
v1put = bond_option1.value(settlement_date, discount_curve, model1)
bond_option2 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model2 = HWTree(sigma, a, num_time_steps,
FinHWEuropeanCalcType.EXPIRY_ONLY)
v2put = bond_option2.value(settlement_date, discount_curve, model2)
option_type = OptionTypes.EUROPEAN_CALL
bond_option1 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model1 = HWTree(sigma, a, num_time_steps)
v1call = bond_option1.value(settlement_date, discount_curve, model1)
bond_option2 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model2 = HWTree(sigma, a, num_time_steps,
FinHWEuropeanCalcType.EXPIRY_TREE)
v2call = bond_option2.value(settlement_date, discount_curve, model2)
end = time.time()
period = end - start
testCases.print(period, num_time_steps, v1put, v2put, v1call, v2call)
libor_curve = IborSingleCurve(valuation_date, depos, fras, swaps)
return libor_curve
todayDate = Date(20, 6, 2019)
valuation_date = todayDate
start_date = todayDate.add_weekdays(2)
maturity_date = start_date.add_tenor("1Y")
libor_curve = build_curve(todayDate)
model1 = Black(0.20)
model2 = BlackShifted(0.25, 0.0)
model3 = SABR(0.013, 0.5, 0.5, 0.5)
model4 = SABRShifted(0.013, 0.5, 0.5, 0.5, -0.008)
model5 = HWTree(0.30, 0.01)
model6 = Bachelier(0.01)
def test_cap():
capFloorType = FinCapFloorTypes.CAP
k = 0.02
capfloor = IborCapFloor(start_date, maturity_date, capFloorType, k)
cvalue1 = capfloor.value(valuation_date, libor_curve, model1)
cvalue2 = capfloor.value(valuation_date, libor_curve, model2)
cvalue3 = capfloor.value(valuation_date, libor_curve, model3)
cvalue4 = capfloor.value(valuation_date, libor_curve, model4)
cvalue5 = capfloor.value(valuation_date, libor_curve, model5)
cvalue6 = capfloor.value(valuation_date, libor_curve, model6)
assert round(cvalue1, 4) == 28889.2445
def test_IborSwaptionQLExample():
valuation_date = Date(4, 3, 2014)
settlement_date = Date(4, 3, 2014)
depoDCCType = DayCountTypes.THIRTY_E_360_ISDA
depos = []
depo = IborDeposit(settlement_date, "1W", 0.0023, depoDCCType)
depos.append(depo)
depo = IborDeposit(settlement_date, "1M", 0.0023, depoDCCType)
depos.append(depo)
depo = IborDeposit(settlement_date, "3M", 0.0023, depoDCCType)
depos.append(depo)
depo = IborDeposit(settlement_date, "6M", 0.0023, depoDCCType)
depos.append(depo)
# No convexity correction provided so I omit interest rate futures
swaps = []
accType = DayCountTypes.ACT_365F
fixedFreqType = FrequencyTypes.SEMI_ANNUAL
fixed_leg_type = SwapTypes.PAY
swap = IborSwap(settlement_date, "3Y", fixed_leg_type, 0.00790,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "4Y", fixed_leg_type, 0.01200,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "5Y", fixed_leg_type, 0.01570,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "6Y", fixed_leg_type, 0.01865,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "7Y", fixed_leg_type, 0.02160,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "8Y", fixed_leg_type, 0.02350,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "9Y", fixed_leg_type, 0.02540,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "10Y", fixed_leg_type, 0.0273,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "15Y", fixed_leg_type, 0.0297,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "20Y", fixed_leg_type, 0.0316,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "25Y", fixed_leg_type, 0.0335,
fixedFreqType, accType)
swaps.append(swap)
swap = IborSwap(settlement_date, "30Y", fixed_leg_type, 0.0354,
fixedFreqType, accType)
swaps.append(swap)
libor_curve = IborSingleCurve(valuation_date, depos, [], swaps,
InterpTypes.LINEAR_ZERO_RATES)
exercise_date = settlement_date.add_tenor("5Y")
swapMaturityDate = exercise_date.add_tenor("5Y")
swapFixedCoupon = 0.040852
swapFixedFrequencyType = FrequencyTypes.SEMI_ANNUAL
swapFixedDayCountType = DayCountTypes.THIRTY_E_360_ISDA
swapFloatFrequencyType = FrequencyTypes.QUARTERLY
swapFloatDayCountType = DayCountTypes.ACT_360
swapNotional = 1000000
swaptionType = SwapTypes.PAY
swaption = IborSwaption(settlement_date, exercise_date, swapMaturityDate,
swaptionType, swapFixedCoupon,
swapFixedFrequencyType, swapFixedDayCountType,
swapNotional, swapFloatFrequencyType,
swapFloatDayCountType)
testCases.header("MODEL", "VALUE")
model = Black(0.1533)
v = swaption.value(settlement_date, libor_curve, model)
testCases.print(model.__class__, v)
model = BlackShifted(0.1533, -0.008)
v = swaption.value(settlement_date, libor_curve, model)
testCases.print(model.__class__, v)
model = SABR(0.132, 0.5, 0.5, 0.5)
v = swaption.value(settlement_date, libor_curve, model)
testCases.print(model.__class__, v)
model = SABRShifted(0.352, 0.5, 0.15, 0.15, -0.005)
v = swaption.value(settlement_date, libor_curve, model)
testCases.print(model.__class__, v)
model = HWTree(0.010000000, 0.00000000001)
v = swaption.value(settlement_date, libor_curve, model)
testCases.print(model.__class__, v)
def test_BondOptionAmericanConvergenceONE():
# Build discount curve
settlement_date = Date(1, 12, 2019)
discount_curve = DiscountCurveFlat(settlement_date, 0.05)
# Bond details
issue_date = Date(1, 9, 2014)
maturity_date = Date(1, 9, 2025)
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)
strike_price = 100.0
face = 100.0
testCases.header("TIME", "N", "PUT_AMER", "PUT_EUR", "CALL_AME",
"CALL_EUR")
timeSteps = range(100, 500, 100)
for num_time_steps in timeSteps:
sigma = 0.05
a = 0.1
start = time.time()
option_type = OptionTypes.AMERICAN_PUT
bond_option1 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model1 = HWTree(sigma, a, num_time_steps)
v1put = bond_option1.value(settlement_date, discount_curve, model1)
option_type = OptionTypes.EUROPEAN_PUT
bond_option2 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model2 = HWTree(sigma, a, num_time_steps,
FinHWEuropeanCalcType.EXPIRY_ONLY)
v2put = bond_option2.value(settlement_date, discount_curve, model2)
option_type = OptionTypes.AMERICAN_CALL
bond_option1 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model1 = HWTree(sigma, a, num_time_steps)
v1call = bond_option1.value(settlement_date, discount_curve, model1)
option_type = OptionTypes.EUROPEAN_CALL
bond_option2 = BondOption(bond, expiry_date, strike_price, face,
option_type)
model2 = HWTree(sigma, a, num_time_steps,
FinHWEuropeanCalcType.EXPIRY_TREE)
v2call = bond_option2.value(settlement_date, discount_curve, model2)
end = time.time()
period = end - start
testCases.print(period, num_time_steps, v1put, v2put, v1call, v2call)
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.add_tenor("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.add_tenor("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 = HWTree(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 = HWTree(sigma, a, num_steps)
start = time.time()
europeanCallBondOption = BondOption(bond, expiry_date, K, face,
OptionTypes.EUROPEAN_CALL)
v_ec = europeanCallBondOption.value(settlement_date, discount_curve,
hwModel)
americanCallBondOption = BondOption(bond, expiry_date, K, face,
OptionTypes.AMERICAN_CALL)
v_ac = americanCallBondOption.value(settlement_date, discount_curve,
hwModel)
europeanPutBondOption = BondOption(bond, expiry_date, K, face,
OptionTypes.EUROPEAN_PUT)
v_ep = europeanPutBondOption.value(settlement_date, discount_curve,
hwModel)
americanPutBondOption = BondOption(bond, expiry_date, K, face,
OptionTypes.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_HullWhiteExampleTwo():
# HULL BOOK ZERO COUPON BOND EXAMPLE 28.1 SEE TABLE 28.3
# Replication may not be exact as I am using dates rather than times
zeroDays = [
0, 3, 31, 62, 94, 185, 367, 731, 1096, 1461, 1826, 2194, 2558, 2922,
3287, 3653
]
zero_rates = [
5.0, 5.01772, 4.98282, 4.97234, 4.96157, 4.99058, 5.09389, 5.79733,
6.30595, 6.73464, 6.94816, 7.08807, 7.27527, 7.30852, 7.39790, 7.49015
]
times = np.array(zeroDays) / 365.0
zeros = np.array(zero_rates) / 100.0
dfs = np.exp(-zeros * times)
start_date = Date(1, 12, 2019)
sigma = 0.01
a = 0.1
strike = 63.0
face = 100.0
expiry_date = start_date.add_tenor("3Y")
maturity_date = start_date.add_tenor("9Y")
texp = (expiry_date - start_date) / gDaysInYear
tmat = (maturity_date - start_date) / gDaysInYear
num_time_steps = None
model = HWTree(sigma, a, num_time_steps)
vAnal = model.option_on_zcb(texp, tmat, strike, face, times, dfs)
num_time_steps = 200
model = HWTree(sigma, a, num_time_steps)
model.build_tree(texp, times, dfs)
vTree1 = model.option_on_zero_coupon_bond_tree(texp, tmat, strike, face)
model = HWTree(sigma, a, num_time_steps + 1)
model.build_tree(texp, times, dfs)
vTree2 = model.option_on_zero_coupon_bond_tree(texp, tmat, strike, face)
vTreeCall = (vTree1['call'] + vTree2['call']) / 2.0
vTreePut = (vTree1['put'] + vTree2['put']) / 2.0
assert round(vTreeCall, 4) == 1.0450
assert round(vAnal['call'], 4) == 1.0448
assert round(vTreePut, 4) == 1.8237
assert round(vAnal['put'], 4) == 1.8239
