def test_FinDateTenors():
startDate = FinDate(2018, 2, 23)
tenor = "5d"
print(tenor, startDate.addTenor(tenor))
tenor = "7D"
print(tenor, startDate.addTenor(tenor))
tenor = "1W"
print(tenor, startDate.addTenor(tenor))
tenor = "4W"
print(tenor, startDate.addTenor(tenor))
tenor = "1M"
print(tenor, startDate.addTenor(tenor))
tenor = "24M"
print(tenor, startDate.addTenor(tenor))
tenor = "2Y"
print(tenor, startDate.addTenor(tenor))
tenor = "10y"
print(tenor, startDate.addTenor(tenor))
tenor = "0m"
print(tenor, startDate.addTenor(tenor))
tenor = "20Y"
print(tenor, startDate.addTenor(tenor))
def test_FinDateTenors():
startDate = FinDate(23, 2, 2018)
testCases.header("TENOR", "DATE")
tenor = "5d"
testCases.print(tenor, startDate.addTenor(tenor))
tenor = "7D"
testCases.print(tenor, startDate.addTenor(tenor))
tenor = "1W"
testCases.print(tenor, startDate.addTenor(tenor))
tenor = "4W"
testCases.print(tenor, startDate.addTenor(tenor))
tenor = "1M"
testCases.print(tenor, startDate.addTenor(tenor))
tenor = "24M"
testCases.print(tenor, startDate.addTenor(tenor))
tenor = "2Y"
testCases.print(tenor, startDate.addTenor(tenor))
tenor = "10y"
testCases.print(tenor, startDate.addTenor(tenor))
tenor = "0m"
testCases.print(tenor, startDate.addTenor(tenor))
tenor = "20Y"
testCases.print(tenor, startDate.addTenor(tenor))
def test_BlackKarasinskiExampleTwo():
# Valuation of a European option on a coupon bearing bond
# This follows example in Fig 28.11 of John Hull's book but does not
# have the exact same dt so there are some differences
settlementDate = FinDate(1, 12, 2019)
expiryDate = settlementDate.addTenor("18m")
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(maturityDate, coupon, frequencyType, accrualType)
bond.calculateFlowDates(settlementDate)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
for flowDate in bond._flowDates:
flowTime = (flowDate - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
strikePrice = 105.0
face = 100.0
tmat = (maturityDate - settlementDate) / gDaysInYear
texp = (expiryDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 20)
dfs = np.exp(-0.05 * times)
curve = FinDiscountCurve(settlementDate, times, dfs)
price = bond.fullPriceFromDiscountCurve(settlementDate, curve)
print("Fixed Income Price:", price)
sigma = 0.20
a = 0.05
# Test convergence
numStepsList = [100] #,101,200,300,400,500,600,700,800,900,1000]
isAmerican = True
treeVector = []
for numTimeSteps in numStepsList:
start = time.time()
model = FinModelRatesBlackKarasinski(a, sigma)
model.buildTree(tmat, int(numTimeSteps), times, dfs)
v = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows,
isAmerican)
end = time.time()
period = end - start
treeVector.append(v[0])
print(numTimeSteps, v, period)
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
]
zeroRates = [
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(zeroRates) / 100.0
dfs = np.exp(-zeros * times)
startDate = FinDate(1, 12, 2019)
sigma = 0.01
a = 0.1
strike = 63.0
face = 100.0
expiryDate = startDate.addTenor("3Y")
maturityDate = startDate.addTenor("9Y")
texp = (expiryDate - startDate) / gDaysInYear
tmat = (maturityDate - startDate) / gDaysInYear
model = FinHullWhiteRateModel(a, sigma)
vAnal = model.optionOnZeroCouponBond(texp, tmat, strike, face, times, dfs)
# Test convergence
numStepsList = range(100, 500, 10)
analVector = []
treeVector = []
for numTimeSteps in numStepsList:
start = time.time()
model.buildTree(texp, numTimeSteps, times, dfs)
vTree = model.optionOnZeroCouponBond_Tree(texp, tmat, strike, face)
end = time.time()
period = end - start
treeVector.append(vTree[1])
analVector.append(vAnal[1])
print(numTimeSteps, vTree, vAnal, period)
plt.plot(numStepsList, treeVector)
plt.plot(numStepsList, analVector)
def test_FinBondMortgage():
principal = 130000
startDate = FinDate(23, 2, 2018)
endDate = startDate.addTenor("10Y")
mortgage = FinBondMortgage(startDate, endDate, principal)
rate = 0.035
mortgage.generateFlows(rate, FinBondMortgageTypes.REPAYMENT)
numFlows = len(mortgage._schedule._adjustedDates)
testCases.header("PAYMENT DATE", "INTEREST", "PRINCIPAL", "OUTSTANDING",
"TOTAL")
for i in range(0, numFlows):
testCases.print(mortgage._schedule._adjustedDates[i],
mortgage._interestFlows[i],
mortgage._principalFlows[i],
mortgage._principalRemaining[i],
mortgage._totalFlows[i])
mortgage.generateFlows(rate, FinBondMortgageTypes.INTEREST_ONLY)
testCases.header("PAYMENT DATE", "INTEREST", "PRINCIPAL", "OUTSTANDING",
"TOTAL")
for i in range(0, numFlows):
testCases.print(mortgage._schedule._adjustedDates[i],
mortgage._interestFlows[i],
mortgage._principalFlows[i],
mortgage._principalRemaining[i],
mortgage._totalFlows[i])
def test_FinScheduleAlignmentEff31():
''' EOM schedule so all unadjusted dates fall on month end.'''
eomFlag = True
valuationDate = FinDate(29, 7, 2006)
effDate = valuationDate.addTenor("2D")
freqType = FinFrequencyTypes.SEMI_ANNUAL
busDayAdjustType = FinBusDayAdjustTypes.MODIFIED_FOLLOWING
dateGenRuleType = FinDateGenRuleTypes.BACKWARD
calendarType = FinCalendarTypes.UNITED_STATES
adjustTerminationDate = True
matDate1 = effDate.addTenor("4Y")
matDate2 = effDate.addTenor("50Y")
# print(matDate1, matDate2)
sched1 = FinSchedule(effDate, matDate1, freqType, calendarType,
busDayAdjustType, dateGenRuleType,
adjustTerminationDate, eomFlag)
sched2 = FinSchedule(effDate, matDate2, freqType, calendarType,
busDayAdjustType, dateGenRuleType,
adjustTerminationDate, eomFlag)
# print(sched1._adjustedDates)
# print(sched2._adjustedDates[:len(sched1._adjustedDates)])
compare = (sched1._adjustedDates[-1] == sched2._adjustedDates[
len(sched1._adjustedDates) - 1])
assert (compare == True)
def test_FinScheduleAlignmentLeapYearNotEOM():
''' Effective date on leap year. Not EOM. '''
eomFlag = False
valuationDate = FinDate(26, 2, 2006)
effDate = valuationDate.addTenor("2D")
freqType = FinFrequencyTypes.SEMI_ANNUAL
busDayAdjustType = FinBusDayAdjustTypes.MODIFIED_FOLLOWING
dateGenRuleType = FinDateGenRuleTypes.BACKWARD
calendarType = FinCalendarTypes.UNITED_STATES
adjustTerminationDate = True
matDate1 = effDate.addTenor("4Y")
matDate2 = effDate.addTenor("50Y")
# print(matDate1, matDate2)
sched1 = FinSchedule(effDate, matDate1, freqType, calendarType,
busDayAdjustType, dateGenRuleType,
adjustTerminationDate, eomFlag)
sched2 = FinSchedule(effDate, matDate2, freqType, calendarType,
busDayAdjustType, dateGenRuleType,
adjustTerminationDate, eomFlag)
# print(sched1._adjustedDates)
# print(sched2._adjustedDates[:len(sched1._adjustedDates)])
compare = (sched1._adjustedDates[-1] == sched2._adjustedDates[
len(sched1._adjustedDates) - 1])
assert (compare == True)
def test_FinBondOption():
settlementDate = FinDate(1, 12, 2019)
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(maturityDate, coupon, frequencyType, accrualType)
tmat = (maturityDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 20)
dfs = np.exp(-0.05 * times)
discountCurve = FinDiscountCurve(settlementDate, times, dfs)
expiryDate = settlementDate.addTenor("18m")
strikePrice = 105.0
face = 100.0
optionType = FinBondOptionTypes.AMERICAN_CALL
price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
print("Fixed Income Price:", price)
for strikePrice in [90, 95, 100, 105, 110]:
sigma = 0.01
a = 0.1
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesHullWhite(a, sigma)
v = bondOption.value(settlementDate, discountCurve, model)
print("HW", strikePrice, v)
for strikePrice in [90, 95, 100, 105, 110]:
sigma = 0.20
a = 0.05
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBlackKarasinski(a, sigma)
v = bondOption.value(settlementDate, discountCurve, model)
print("BK", strikePrice, v)
def test_FinBondMortgage():
principal = 130000
startDate = FinDate(23, 2, 2018)
endDate = startDate.addTenor("10Y")
mortgage = FinBondMortgage(startDate, endDate, principal)
rate = 0.035
mortgage.generateFlows(rate, FinBondMortgageType.REPAYMENT)
mortgage.print()
mortgage.generateFlows(rate, FinBondMortgageType.INTEREST_ONLY)
mortgage.print()
def test_FinScheduleAlignment(eomFlag):
valuationDate = FinDate(29, 3, 2005)
effDate = valuationDate.addTenor("2d")
freqType = FinFrequencyTypes.SEMI_ANNUAL
busDayAdjustType = FinBusDayAdjustTypes.MODIFIED_FOLLOWING
dateGenRuleType = FinDateGenRuleTypes.BACKWARD
calendarType = FinCalendarTypes.UNITED_STATES
adjustTerminationDate = False
matDate1 = effDate.addTenor("4Y")
matDate2 = effDate.addTenor("50Y")
# print(matDate1)
# print(matDate2)
myCal = FinCalendar(calendarType)
adjustedMatDate1 = myCal.adjust(matDate1, busDayAdjustType)
adjustedMatDate2 = myCal.adjust(matDate2, busDayAdjustType)
# print(adjustedMatDate1)
# print(adjustedMatDate2)
sched1 = FinSchedule(effDate,
adjustedMatDate1,
freqType,
calendarType,
busDayAdjustType,
dateGenRuleType,
adjustTerminationDate,
eomFlag)
# print(sched1)
sched2 = FinSchedule(effDate,
adjustedMatDate2,
freqType,
calendarType,
busDayAdjustType,
dateGenRuleType,
adjustTerminationDate,
eomFlag)
compare = (sched1._adjustedDates[-1] == sched2._adjustedDates[len(sched1._adjustedDates)-1])
assert(compare == eomFlag)
def test_HullWhiteCallableBond():
# Valuation of a European option on a coupon bearing bond
settlementDate = FinDate(1, 12, 2019)
issueDate = FinDate(1, 12, 2018)
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, frequencyType, accrualType)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
for flowDate in bond._flowDates[1:]:
if flowDate > settlementDate:
flowTime = (flowDate - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
###########################################################################
# Set up the call and put times and prices
###########################################################################
callDates = []
callPrices = []
callPx = 120.0
callDates.append(settlementDate.addTenor("2Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("3Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("4Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("5Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("6Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("7Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("8Y"))
callPrices.append(callPx)
callTimes = []
for dt in callDates:
t = (dt - settlementDate) / gDaysInYear
callTimes.append(t)
putDates = []
putPrices = []
putPx = 98.0
putDates.append(settlementDate.addTenor("2Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("3Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("4Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("5Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("6Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("7Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("8Y"))
putPrices.append(putPx)
putTimes = []
for dt in putDates:
t = (dt - settlementDate) / gDaysInYear
putTimes.append(t)
###########################################################################
tmat = (maturityDate - settlementDate) / gDaysInYear
curve = FinDiscountCurveFlat(settlementDate, 0.05,
FinFrequencyTypes.CONTINUOUS)
dfs = []
times = []
for dt in bond._flowDates:
if dt > settlementDate:
t = (dt - settlementDate) / gDaysInYear
df = curve.df(dt)
times.append(t)
dfs.append(df)
dfs = np.array(dfs)
times = np.array(times)
###########################################################################
v1 = bond.cleanPriceFromDiscountCurve(settlementDate, curve)
sigma = 0.02 # basis point volatility
a = 0.01
# Test convergence
numStepsList = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]
tmat = (maturityDate - settlementDate) / gDaysInYear
testCases.header("NUMSTEPS", "BOND_ONLY", "CALLABLE_BOND", "TIME")
for numTimeSteps in numStepsList:
start = time.time()
model = FinModelRatesHW(sigma, a, numTimeSteps)
model.buildTree(tmat, times, dfs)
v2 = model.callablePuttableBond_Tree(couponTimes, couponFlows,
callTimes, callPrices, putTimes,
putPrices, 100.0)
end = time.time()
period = end - start
testCases.print(numTimeSteps, v1, v2, period)
def test_HullWhiteCallableBond():
# Valuation of a European option on a coupon bearing bond
settlementDate = FinDate(1, 12, 2019)
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(maturityDate, coupon, frequencyType, accrualType)
bond.calculateFlowDates(settlementDate)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
for flowDate in bond._flowDates[1:]:
flowTime = (flowDate - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
###########################################################################
# Set up the call and put times and prices
###########################################################################
callDates = []
callPrices = []
callPx = 120.0
callDates.append(settlementDate.addTenor("5Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("6Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("7Y"))
callPrices.append(callPx)
callDates.append(settlementDate.addTenor("8Y"))
callPrices.append(callPx)
callTimes = []
for dt in callDates:
t = (dt - settlementDate) / gDaysInYear
callTimes.append(t)
putDates = []
putPrices = []
putPx = 98.0
putDates.append(settlementDate.addTenor("5Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("6Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("7Y"))
putPrices.append(putPx)
putDates.append(settlementDate.addTenor("8Y"))
putPrices.append(putPx)
putTimes = []
for dt in putDates:
t = (dt - settlementDate) / gDaysInYear
putTimes.append(t)
###########################################################################
tmat = (maturityDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 20)
dfs = np.exp(-0.05 * times)
curve = FinDiscountCurve(settlementDate, times, dfs)
###########################################################################
v1 = bond.fullPriceFromDiscountCurve(settlementDate, curve)
sigma = 0.02 # basis point volatility
a = 0.1
# Test convergence
numStepsList = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]
tmat = (maturityDate - settlementDate) / gDaysInYear
print("NUMSTEPS", "BOND_ONLY", "CALLABLE_BOND", "TIME")
for numTimeSteps in numStepsList:
start = time.time()
model = FinModelRatesHullWhite(a, sigma)
model.buildTree(tmat, numTimeSteps, times, dfs)
v2 = model.callablePuttableBond_Tree(couponTimes, couponFlows,
callTimes, callPrices, putTimes,
putPrices)
end = time.time()
period = end - start
print(numTimeSteps, v1, v2, period)
if 1 == 0:
print("RT")
printTree(model._rt, 5)
print("BOND")
printTree(model._bondValues, 5)
print("OPTION")
printTree(model._optionValues, 5)
def testFinLiborCashSettledSwaption():
testCases.header("LABEL", "VALUE")
valuationDate = FinDate(1, 1, 2020)
settlementDate = FinDate(1, 1, 2020)
depoDCCType = FinDayCountTypes.THIRTY_E_360_ISDA
depos = []
depo = FinLiborDeposit(settlementDate, "1W", 0.0023, depoDCCType)
depos.append(depo)
depo = FinLiborDeposit(settlementDate, "1M", 0.0023, depoDCCType)
depos.append(depo)
depo = FinLiborDeposit(settlementDate, "3M", 0.0023, depoDCCType)
depos.append(depo)
depo = FinLiborDeposit(settlementDate, "6M", 0.0023, depoDCCType)
depos.append(depo)
# No convexity correction provided so I omit interest rate futures
settlementDate = FinDate(2, 1, 2020)
swaps = []
accType = FinDayCountTypes.ACT_365F
fixedFreqType = FinFrequencyTypes.SEMI_ANNUAL
swapType = FinLiborSwapTypes.PAYER
swap = FinLiborSwap(settlementDate, "3Y", swapType, 0.00790, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "4Y", swapType, 0.01200, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "5Y", swapType, 0.01570, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "6Y", swapType, 0.01865, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "7Y", swapType, 0.02160, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "8Y", swapType, 0.02350, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "9Y", swapType, 0.02540, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "10Y", swapType, 0.0273, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "15Y", swapType, 0.0297, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "20Y", swapType, 0.0316, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "25Y", swapType, 0.0335, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "30Y", swapType, 0.0354, fixedFreqType,
accType)
swaps.append(swap)
liborCurve = FinLiborCurve(valuationDate, depos, [], swaps,
FinInterpTypes.LINEAR_ZERO_RATES)
exerciseDate = settlementDate.addTenor("5Y")
swapMaturityDate = exerciseDate.addTenor("5Y")
swapFixedCoupon = 0.040852
swapFixedFrequencyType = FinFrequencyTypes.SEMI_ANNUAL
swapFixedDayCountType = FinDayCountTypes.THIRTY_E_360_ISDA
swapFloatFrequencyType = FinFrequencyTypes.QUARTERLY
swapFloatDayCountType = FinDayCountTypes.ACT_360
swapNotional = 1000000
swaptionType = FinLiborSwapTypes.PAYER
swaption = FinLiborSwaption(settlementDate, exerciseDate, swapMaturityDate,
swaptionType, swapFixedCoupon,
swapFixedFrequencyType, swapFixedDayCountType,
swapNotional, swapFloatFrequencyType,
swapFloatDayCountType)
model = FinModelBlack(0.1533)
v = swaption.value(settlementDate, liborCurve, model)
testCases.print("Swaption No-Arb Value:", v)
fwdSwapRate = liborCurve.swapRate(valuationDate, swapMaturityDate,
swapFixedFrequencyType,
swapFixedDayCountType)
testCases.print("Fwd Swap Rate:", fwdSwapRate)
model = FinModelBlack(0.1533)
v = swaption.cashSettledValue(valuationDate, liborCurve, fwdSwapRate,
model)
testCases.print("Swaption Cash Settled Value:", v)
def test_FinLiborSwaptionQLExample():
# valuationDate = FinDate(28, 2, 2014)
settlementDate = FinDate(4, 3, 2014)
depoDCCType = FinDayCountTypes.THIRTY_E_360_ISDA
depos = []
depo = FinLiborDeposit(settlementDate, "1W", 0.0023, depoDCCType)
depos.append(depo)
depo = FinLiborDeposit(settlementDate, "1M", 0.0023, depoDCCType)
depos.append(depo)
depo = FinLiborDeposit(settlementDate, "3M", 0.0023, depoDCCType)
depos.append(depo)
depo = FinLiborDeposit(settlementDate, "6M", 0.0023, depoDCCType)
depos.append(depo)
# No convexity correction provided so I omit interest rate futures
swaps = []
accType = FinDayCountTypes.ACT_365F
fixedFreqType = FinFrequencyTypes.SEMI_ANNUAL
swapType = FinLiborSwapTypes.PAYER
swap = FinLiborSwap(settlementDate, "3Y", swapType, 0.00790, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "4Y", swapType, 0.01200, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "5Y", swapType, 0.01570, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "6Y", swapType, 0.01865, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "7Y", swapType, 0.02160, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "8Y", swapType, 0.02350, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "9Y", swapType, 0.02540, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "10Y", swapType, 0.0273, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "15Y", swapType, 0.0297, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "20Y", swapType, 0.0316, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "25Y", swapType, 0.0335, fixedFreqType,
accType)
swaps.append(swap)
swap = FinLiborSwap(settlementDate, "30Y", swapType, 0.0354, fixedFreqType,
accType)
swaps.append(swap)
liborCurve = FinLiborCurve(settlementDate, depos, [], swaps,
FinInterpTypes.LINEAR_ZERO_RATES)
exerciseDate = settlementDate.addTenor("5Y")
swapMaturityDate = exerciseDate.addTenor("5Y")
swapFixedCoupon = 0.040852
swapFixedFrequencyType = FinFrequencyTypes.SEMI_ANNUAL
swapFixedDayCountType = FinDayCountTypes.THIRTY_E_360_ISDA
swapFloatFrequencyType = FinFrequencyTypes.QUARTERLY
swapFloatDayCountType = FinDayCountTypes.ACT_360
swapNotional = 1000000
swaptionType = FinLiborSwapTypes.PAYER
swaption = FinLiborSwaption(settlementDate, exerciseDate, swapMaturityDate,
swaptionType, swapFixedCoupon,
swapFixedFrequencyType, swapFixedDayCountType,
swapNotional, swapFloatFrequencyType,
swapFloatDayCountType)
testCases.header("MODEL", "VALUE")
model = FinModelBlack(0.1533)
v = swaption.value(settlementDate, liborCurve, model)
testCases.print(model.__class__, v)
model = FinModelBlackShifted(0.1533, -0.008)
v = swaption.value(settlementDate, liborCurve, model)
testCases.print(model.__class__, v)
model = FinModelSABR(0.132, 0.5, 0.5, 0.5)
v = swaption.value(settlementDate, liborCurve, model)
testCases.print(model.__class__, v)
model = FinModelSABRShifted(0.352, 0.5, 0.15, 0.15, -0.005)
v = swaption.value(settlementDate, liborCurve, model)
testCases.print(model.__class__, v)
model = FinModelRatesHW(0.010000000, 0.00000000001)
v = swaption.value(settlementDate, liborCurve, model)
testCases.print(model.__class__, v)
def test_HullWhiteBondOption():
# Valuation of a European option on a coupon bearing bond
settlementDate = FinDate(1, 12, 2019)
expiryDate = settlementDate.addTenor("18m")
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(maturityDate, coupon, frequencyType, accrualType)
bond.calculateFlowDates(settlementDate)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
for flowDate in bond._flowDates[1:]:
flowTime = (flowDate - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
strikePrice = 105.0
face = 100.0
tmat = (maturityDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 20)
dfs = np.exp(-0.05 * times)
curve = FinDiscountCurve(settlementDate, times, dfs)
price = bond.fullPriceFromDiscountCurve(settlementDate, curve)
print("Spot Bond Price:", price)
price = bond.fullPriceFromDiscountCurve(expiryDate, curve)
print("Fwd Bond Price:", price)
sigma = 0.01
a = 0.1
# Test convergence
numStepsList = [100, 200, 300, 400, 500]
texp = (expiryDate - settlementDate) / gDaysInYear
print("NUMSTEPS", "FAST TREE", "FULLTREE", "TIME")
for numTimeSteps in numStepsList:
start = time.time()
model = FinModelRatesHullWhite(a, sigma)
model.buildTree(texp, numTimeSteps, times, dfs)
americanExercise = False
v1 = model.americanBondOption_Tree(texp, strikePrice, face,
couponTimes, couponFlows,
americanExercise)
v2 = model.europeanBondOption_Tree(texp, strikePrice, face,
couponTimes, couponFlows)
end = time.time()
period = end - start
print(numTimeSteps, v1, v2, period)
# plt.plot(numStepsList, treeVector)
if 1 == 0:
print("RT")
printTree(model._rt, 5)
print("BOND")
printTree(model._bondValues, 5)
print("OPTION")
printTree(model._optionValues, 5)
v = model.europeanBondOption_Jamshidian(texp, strikePrice, face,
couponTimes, couponFlows, times,
dfs)
print("EUROPEAN BOND JAMSHIDIAN DECOMP", v)
def test_FinBondOption():
settlementDate = FinDate(1, 12, 2019)
issueDate = FinDate(1, 12, 2018)
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
freqType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType)
times = np.linspace(0, 10.0, 21)
dfs = np.exp(-0.05 * times)
dates = settlementDate.addYears(times)
discountCurve = FinDiscountCurve(settlementDate, dates, dfs)
expiryDate = settlementDate.addTenor("18m")
strikePrice = 105.0
face = 100.0
###########################################################################
strikes = [80, 85, 90, 95, 100, 105, 110, 115, 120]
optionType = FinOptionTypes.EUROPEAN_CALL
testCases.header("LABEL", "VALUE")
price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve)
testCases.print("Fixed Income Price:", price)
numTimeSteps = 100
testCases.banner("HW EUROPEAN CALL")
testCases.header("STRIKE", "VALUE")
for strikePrice in strikes:
sigma = 0.01
a = 0.1
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesHW(sigma, a, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print(strikePrice, v)
###########################################################################
optionType = FinOptionTypes.AMERICAN_CALL
price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve)
testCases.header("LABEL", "VALUE")
testCases.print("Fixed Income Price:", price)
testCases.banner("HW AMERICAN CALL")
testCases.header("STRIKE", "VALUE")
for strikePrice in strikes:
sigma = 0.01
a = 0.1
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesHW(sigma, a)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print(strikePrice, v)
###########################################################################
optionType = FinOptionTypes.EUROPEAN_PUT
testCases.banner("HW EUROPEAN PUT")
testCases.header("STRIKE", "VALUE")
price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve)
for strikePrice in strikes:
sigma = 0.01
a = 0.1
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesHW(sigma, a)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print(strikePrice, v)
###########################################################################
optionType = FinOptionTypes.AMERICAN_PUT
testCases.banner("HW AMERICAN PUT")
testCases.header("STRIKE", "VALUE")
price = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve)
for strikePrice in strikes:
sigma = 0.02
a = 0.1
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesHW(sigma, a)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print(strikePrice, v)
def test_FinBondOptionZEROVOLConvergence():
# Build discount curve
settlementDate = FinDate(1, 12, 2019) # CHANGED
rate = 0.05
discountCurve = FinDiscountCurveFlat(settlementDate, rate,
FinFrequencyTypes.ANNUAL)
# Bond details
issueDate = FinDate(1, 9, 2015)
maturityDate = FinDate(1, 9, 2025)
coupon = 0.06
freqType = FinFrequencyTypes.ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType)
# Option Details
expiryDate = settlementDate.addTenor("18m") # FinDate(1, 12, 2021)
# print("EXPIRY:", expiryDate)
face = 100.0
dfExpiry = discountCurve.df(expiryDate)
spotCleanValue = bond.cleanPriceFromDiscountCurve(settlementDate,
discountCurve)
fwdCleanValue = bond.cleanPriceFromDiscountCurve(expiryDate, discountCurve)
# print("BOND SpotCleanBondPx", spotCleanValue)
# print("BOND FwdCleanBondPx", fwdCleanValue)
# print("BOND Accrued:", bond._accruedInterest)
spotCleanValue = bond.cleanPriceFromDiscountCurve(settlementDate,
discountCurve)
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, 200)
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 numSteps in numTimeSteps:
sigma = 0.0000001
model = FinModelRatesBDT(sigma, numSteps)
optionType = FinOptionTypes.EUROPEAN_CALL
bondOption1 = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
v1 = bondOption1.value(settlementDate, discountCurve, model)
optionType = FinOptionTypes.AMERICAN_CALL
bondOption2 = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
v2 = bondOption2.value(settlementDate, discountCurve, model)
optionType = FinOptionTypes.EUROPEAN_PUT
bondOption3 = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
v3 = bondOption3.value(settlementDate, discountCurve, model)
optionType = FinOptionTypes.AMERICAN_PUT
bondOption4 = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
v4 = bondOption4.value(settlementDate, discountCurve, model)
testCases.print(strikePrice, numSteps, callIntrinsic,
callIntrinsicPV, v1, v2, putIntrinsic,
putIntrinsicPV, v3, v4)
def test_FinBondOptionAmericanConvergenceTWO():
# Build discount curve
settlementDate = FinDate(1, 12, 2019)
discountCurve = FinDiscountCurveFlat(settlementDate, 0.05,
FinFrequencyTypes.CONTINUOUS)
# Bond details
issueDate = FinDate(1, 9, 2014)
maturityDate = FinDate(1, 9, 2025)
coupon = 0.05
freqType = FinFrequencyTypes.ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType)
expiryDate = settlementDate.addTenor("18m")
face = 100.0
spotValue = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
testCases.header("LABEL", "VALUE")
testCases.print("BOND PRICE", spotValue)
testCases.header("TIME", "N", "EUR_CALL", "AMER_CALL", "EUR_PUT",
"AMER_PUT")
sigma = 0.2
model = FinModelRatesBDT(sigma)
K = 101.0
vec_ec = []
vec_ac = []
vec_ep = []
vec_ap = []
if 1 == 1:
K = 100.0
bkModel = FinModelRatesBDT(sigma, 100)
europeanCallBondOption = FinBondOption(bond, expiryDate, K, face,
FinOptionTypes.EUROPEAN_CALL)
v_ec = europeanCallBondOption.value(settlementDate, discountCurve,
model)
testCases.header("LABEL", "VALUE")
testCases.print("OPTION", v_ec)
numStepsVector = range(100, 100, 1) # should be 100-400
for numSteps in numStepsVector:
bkModel = FinModelRatesBDT(sigma, numSteps)
start = time.time()
europeanCallBondOption = FinBondOption(bond, expiryDate, K, face,
FinOptionTypes.EUROPEAN_CALL)
v_ec = europeanCallBondOption.value(settlementDate, discountCurve,
bkModel)
americanCallBondOption = FinBondOption(bond, expiryDate, K, face,
FinOptionTypes.AMERICAN_CALL)
v_ac = americanCallBondOption.value(settlementDate, discountCurve,
bkModel)
europeanPutBondOption = FinBondOption(bond, expiryDate, K, face,
FinOptionTypes.EUROPEAN_PUT)
v_ep = europeanPutBondOption.value(settlementDate, discountCurve,
bkModel)
americanPutBondOption = FinBondOption(bond, expiryDate, K, face,
FinOptionTypes.AMERICAN_PUT)
v_ap = americanPutBondOption.value(settlementDate, discountCurve,
bkModel)
end = time.time()
period = end - start
testCases.print(period, numSteps, 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(numStepsVector, vec_ec, label="European Call")
plt.legend()
plt.figure()
plt.plot(numStepsVector, vec_ac, label="American Call")
plt.legend()
plt.figure()
plt.plot(numStepsVector, vec_ep, label="European Put")
plt.legend()
plt.figure()
plt.plot(numStepsVector, vec_ap, label="American Put")
plt.legend()
def test_HullWhiteBondOption():
# Valuation of a European option on a coupon bearing bond
settlementDate = FinDate(1, 12, 2019)
issueDate = FinDate(1, 12, 2018)
expiryDate = settlementDate.addTenor("18m")
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, frequencyType, accrualType)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
numFlows = len(bond._flowDates)
for i in range(1, numFlows):
pcd = bond._flowDates[i - 1]
ncd = bond._flowDates[i]
if ncd > settlementDate:
if len(couponTimes) == 0:
flowTime = (pcd - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
flowTime = (ncd - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
strikePrice = 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 = FinModelRatesHW(sigma, a, None)
# Test convergence
numStepsList = range(20, 500, 10)
texp = (expiryDate - settlementDate) / gDaysInYear
vJam = model.europeanBondOptionJamshidian(texp, strikePrice, face,
couponTimes, couponFlows, 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", "EXPIRY_ONLY", "EXPIRY_TREE", "JAMSHIDIAN",
"TIME")
for numTimeSteps in numStepsList:
start = time.time()
model = FinModelRatesHW(sigma, a, numTimeSteps,
FinHWEuropeanCalcType.EXPIRY_ONLY)
model.buildTree(texp, times, dfs)
exerciseType = FinOptionExerciseTypes.EUROPEAN
v1 = model.bondOption(texp, strikePrice, face, couponTimes,
couponFlows, exerciseType)
model = FinModelRatesHW(sigma, a, numTimeSteps,
FinHWEuropeanCalcType.EXPIRY_TREE)
model.buildTree(texp, times, dfs)
v2 = model.bondOption(texp, strikePrice, face, couponTimes,
couponFlows, exerciseType)
end = time.time()
period = end - start
testCases.print(numTimeSteps, v1, v2, vJam, period)
# plt.plot(numStepsList, treeVector)
if 1 == 0:
print("RT")
printTree(model._rt, 5)
print("BOND")
printTree(model._bondValues, 5)
print("OPTION")
printTree(model._optionValues, 5)
print("ADD WORKDAYS")
print(dt1, dt1.addWorkDays(2))
# The weekend has now been skipped
# To add a month do
print("ADD MONTHS")
print(dt1, dt1.addMonths(2))
# An invalid date will throw an error
# dt5 = FinDate(2019, 1, 31)
# print(dt5)
# You can use tenors - a number and a 'd', 'm' or 'y' in upper or lower case
print("TENORS")
print(dt1.addTenor("1d"))
print(dt1.addTenor("2D"))
print(dt1.addTenor("3M"))
print(dt1.addTenor("4m"))
print(dt1.addTenor("5Y"))
print(dt1.addTenor("6y"))
# You can subtract dates
print("SUBTRACT DATES")
dt6 = dt1.addTenor("5Y")
dt7 = dt1.addTenor("10Y")
dd = dt7 - dt6
print(dt6, dt7, dd)
# check if a date is on a weekend
print("WEEKEND TEST")
def test_FinBondOption():
settlementDate = FinDate(1, 12, 2019)
issueDate = FinDate(1, 12, 2018)
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
freqType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType)
tmat = (maturityDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 20)
dates = settlementDate.addYears(times)
dfs = np.exp(-0.05 * times)
discountCurve = FinDiscountCurve(settlementDate, dates, dfs)
expiryDate = settlementDate.addTenor("18m")
strikePrice = 105.0
face = 100.0
###########################################################################
strikes = [80, 90, 100, 110, 120]
optionType = FinOptionTypes.EUROPEAN_CALL
testCases.header("LABEL", "VALUE")
price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
testCases.print("Fixed Income Price:", price)
numTimeSteps = 100
testCases.header("OPTION TYPE AND MODEL", "STRIKE", "VALUE")
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("EUROPEAN CALL - BK", strikePrice, v)
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("EUROPEAN CALL - BK", strikePrice, v)
###########################################################################
optionType = FinOptionTypes.AMERICAN_CALL
price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
testCases.header("LABEL", "VALUE")
testCases.print("Fixed Income Price:", price)
testCases.header("OPTION TYPE AND MODEL", "STRIKE", "VALUE")
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("AMERICAN CALL - BK", strikePrice, v)
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("AMERICAN CALL - BK", strikePrice, v)
###########################################################################
optionType = FinOptionTypes.EUROPEAN_PUT
price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
for strikePrice in strikes:
sigma = 0.01
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("EUROPEAN PUT - BK", strikePrice, v)
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("EUROPEAN PUT - BK", strikePrice, v)
###########################################################################
optionType = FinOptionTypes.AMERICAN_PUT
price = bond.fullPriceFromDiscountCurve(settlementDate, discountCurve)
for strikePrice in strikes:
sigma = 0.02
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("AMERICAN PUT - BK", strikePrice, v)
for strikePrice in strikes:
sigma = 0.20
bondOption = FinBondOption(bond, expiryDate, strikePrice, face,
optionType)
model = FinModelRatesBDT(sigma, numTimeSteps)
v = bondOption.value(settlementDate, discountCurve, model)
testCases.print("AMERICAN PUT - BK", strikePrice, v)
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
]
zeroRates = [
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(zeroRates) / 100.0
dfs = np.exp(-zeros * times)
startDate = FinDate(1, 12, 2019)
sigma = 0.01
a = 0.1
strike = 63.0
face = 100.0
expiryDate = startDate.addTenor("3Y")
maturityDate = startDate.addTenor("9Y")
texp = (expiryDate - startDate) / gDaysInYear
tmat = (maturityDate - startDate) / gDaysInYear
numTimeSteps = None
model = FinModelRatesHW(sigma, a, numTimeSteps)
vAnal = model.optionOnZCB(texp, tmat, strike, face, times, dfs)
# Test convergence
numStepsList = range(100, 500, 50)
analVector = []
treeVector = []
testCases.banner("Comparing option on zero coupon bond analytical vs Tree")
testCases.header("NUMTIMESTEP", "VTREE_CALL", "VTREE_PUT", "VANAL CALL",
"VANAL_PUT", "CALLDIFF", "PUTDIFF", "PERIOD")
for numTimeSteps in numStepsList:
start = time.time()
model = FinModelRatesHW(sigma, a, numTimeSteps)
model.buildTree(texp, times, dfs)
vTree1 = model.optionOnZeroCouponBond_Tree(texp, tmat, strike, face)
model = FinModelRatesHW(sigma, a, numTimeSteps + 1)
model.buildTree(texp, times, dfs)
vTree2 = model.optionOnZeroCouponBond_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(numTimeSteps, vTreeCall, vAnal['call'], vTreePut,
vAnal['put'], diffC, diffP, period)
def test_BDTExampleTwo():
# Valuation of a European option on a coupon bearing bond
# This follows example in Fig 28.11 of John Hull's book (6th Edition)
# but does not have the exact same dt so there are some differences
testCases.banner("===================== FIG 28.11 HULL BOOK =============")
settlementDate = FinDate(1, 12, 2019)
issueDate = FinDate(1, 12, 2015)
expiryDate = settlementDate.addTenor("18m")
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
freqType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, freqType, accrualType)
couponTimes = []
couponFlows = []
cpn = bond._coupon / bond._frequency
numFlows = len(bond._flowDates)
for i in range(1, numFlows):
pcd = bond._flowDates[i - 1]
ncd = bond._flowDates[i]
if pcd < settlementDate and ncd > settlementDate:
flowTime = (pcd - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
for flowDate in bond._flowDates:
if flowDate > settlementDate:
flowTime = (flowDate - settlementDate) / gDaysInYear
couponTimes.append(flowTime)
couponFlows.append(cpn)
couponTimes = np.array(couponTimes)
couponFlows = np.array(couponFlows)
strikePrice = 105.0
face = 100.0
tmat = (maturityDate - settlementDate) / gDaysInYear
texp = (expiryDate - settlementDate) / gDaysInYear
times = np.linspace(0, tmat, 11)
dates = settlementDate.addYears(times)
dfs = np.exp(-0.05 * times)
testCases.header("LABEL", "VALUES")
testCases.print("TIMES:", times)
curve = FinDiscountCurve(settlementDate, dates, dfs)
price = bond.cleanPriceFromDiscountCurve(settlementDate, curve)
testCases.print("Fixed Income Price:", price)
sigma = 0.20
# Test convergence
numStepsList = [5] #[100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]
exerciseType = FinExerciseTypes.AMERICAN
testCases.header("Values")
treeVector = []
for numTimeSteps in numStepsList:
model = FinModelRatesBDT(sigma, numTimeSteps)
model.buildTree(tmat, times, dfs)
v = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows,
exerciseType)
testCases.print(v)
treeVector.append(v['call'])
if PLOT_GRAPHS:
plt.plot(numStepsList, treeVector)
# The value in Hull converges to 0.699 with 100 time steps while I get 0.70
if 1 == 0:
print("RT")
printTree(model._rt, 5)
print("Q")
printTree(model._Q, 5)
def test_FinBondOptionAmericanConvergenceTWO():
# Build discount curve
settlementDate = FinDate(1, 12, 2019)
discountCurve = FinDiscountCurveFlat(settlementDate, 0.05)
# Bond details
issueDate = FinDate(1, 12, 2015)
maturityDate = settlementDate.addTenor("10Y")
coupon = 0.05
frequencyType = FinFrequencyTypes.SEMI_ANNUAL
accrualType = FinDayCountTypes.ACT_ACT_ICMA
bond = FinBond(issueDate, maturityDate, coupon, frequencyType, accrualType)
expiryDate = settlementDate.addTenor("18m")
face = 100.0
spotValue = bond.cleanPriceFromDiscountCurve(settlementDate, discountCurve)
testCases.header("LABEL", "VALUE")
testCases.print("BOND PRICE", spotValue)
testCases.header("PERIOD", "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 = []
numStepsVector = range(10, 500, 10)
for numSteps in numStepsVector:
hwModel = FinModelRatesHW(sigma, a, numSteps)
start = time.time()
europeanCallBondOption = FinBondOption(bond, expiryDate, K, face,
FinOptionTypes.EUROPEAN_CALL)
v_ec = europeanCallBondOption.value(settlementDate, discountCurve,
hwModel)
americanCallBondOption = FinBondOption(bond, expiryDate, K, face,
FinOptionTypes.AMERICAN_CALL)
v_ac = americanCallBondOption.value(settlementDate, discountCurve,
hwModel)
europeanPutBondOption = FinBondOption(bond, expiryDate, K, face,
FinOptionTypes.EUROPEAN_PUT)
v_ep = europeanPutBondOption.value(settlementDate, discountCurve,
hwModel)
americanPutBondOption = FinBondOption(bond, expiryDate, K, face,
FinOptionTypes.AMERICAN_PUT)
v_ap = americanPutBondOption.value(settlementDate, discountCurve,
hwModel)
end = time.time()
period = end - start
testCases.print(period, numSteps, 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(numStepsVector, vec_ac, label="American Call")
plt.legend()
plt.figure()
plt.plot(numStepsVector, vec_ap, label="American Put")
plt.legend()