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import QuantLib as ql
import prettytable as pt
# set up dates
calendar = ql.TARGET()
todaysDate = ql.Date(15, ql.May, 1998)
settlementDate = ql.Date(17, ql.May, 1998)
ql.Settings.instance().evaluationDate = todaysDate
# our options
optType = ql.Option.Put
underlying = 36.0
strike = 40.0
dividendYield = 0.00
riskFreeRate = 0.06
volatility = 0.20
maturity = ql.Date(17, ql.May, 1999)
dayCounter = ql.Actual365Fixed()
print('Option type =', optType)
print('Maturity =', maturity)
print('Underlying price =', underlying)
print('Strike =', strike)
print('Risk-free interest rate =', '{0:%}'.format(riskFreeRate))
print('Dividend yield =', '{0:%}'.format(dividendYield))
print('Volatility =', '{0:%}'.format(volatility))
print()
# show table
tab = pt.PrettyTable(['Method', 'European', 'Bermudan', 'American'])
exerciseDates = ql.DateVector()
for i in range(1, 5):
exerciseDates.push_back(settlementDate + ql.Period(3 * i, ql.Months))
# exerciseDates = [settlementDate+ql.Period(3*i,ql.Months) for i in range(1,5)]
europeanExercise = ql.EuropeanExercise(maturity)
bermudanExercise = ql.BermudanExercise(exerciseDates)
americanExercise = ql.AmericanExercise(settlementDate, maturity)
underlyingH = ql.QuoteHandle(ql.SimpleQuote(underlying))
# bootstrap the yield/dividend/vol curves
flatTermStructure = ql.YieldTermStructureHandle(
ql.FlatForward(settlementDate, riskFreeRate, dayCounter))
flatDividendTS = ql.YieldTermStructureHandle(
ql.FlatForward(settlementDate, dividendYield, dayCounter))
flatVolTS = ql.BlackVolTermStructureHandle(
ql.BlackConstantVol(
settlementDate, calendar, volatility, dayCounter))
payoff = ql.PlainVanillaPayoff(optType, strike)
bsmProcess = ql.BlackScholesMertonProcess(
underlyingH, flatDividendTS, flatTermStructure, flatVolTS)
# options
europeanOption = ql.VanillaOption(payoff, europeanExercise)
bermudanOption = ql.VanillaOption(payoff, bermudanExercise)
americanOption = ql.VanillaOption(payoff, americanExercise)
# Analytic formulas:
# Black-Scholes for European
method = 'Black-Scholes'
europeanOption.setPricingEngine(
ql.AnalyticEuropeanEngine(bsmProcess))
tab.add_row([method, europeanOption.NPV(), 'N/A', 'N/A'])
# semi-analytic Heston for European
method = 'Heston semi-analytic'
hestonProcess = ql.HestonProcess(
flatTermStructure, flatDividendTS, underlyingH,
volatility * volatility, 1.0, volatility * volatility, 0.001, 0.0)
hestonModel = ql.HestonModel(hestonProcess)
europeanOption.setPricingEngine(
ql.AnalyticHestonEngine(hestonModel))
tab.add_row([method, europeanOption.NPV(), 'N/A', 'N/A'])
# semi-analytic Bates for European
method = 'Bates semi-analytic'
batesProcess = ql.BatesProcess(
flatTermStructure, flatDividendTS, underlyingH,
volatility * volatility, 1.0, volatility * volatility,
0.001, 0.0, 1e-14, 1e-14, 1e-14)
batesModel = ql.BatesModel(batesProcess)
europeanOption.setPricingEngine(
ql.BatesEngine(batesModel))
tab.add_row([method, europeanOption.NPV(), 'N/A', 'N/A'])
# Barone-Adesi and Whaley approximation for American
method = 'Barone-Adesi/Whaley'
americanOption.setPricingEngine(
ql.BaroneAdesiWhaleyApproximationEngine(bsmProcess))
tab.add_row([method, 'N/A', 'N/A', americanOption.NPV()])
# Bjerksund and Stensland approximation for American
method = 'Bjerksund/Stensland'
americanOption.setPricingEngine(
ql.BjerksundStenslandApproximationEngine(bsmProcess))
tab.add_row([method, 'N/A', 'N/A', americanOption.NPV()])
# Integral
method = 'Integral'
europeanOption.setPricingEngine(
ql.IntegralEngine(bsmProcess))
tab.add_row([method, europeanOption.NPV(), 'N/A', 'N/A'])
# Finite differences
timeSteps = 801
method = 'Finite differences'
fdengine = ql.FdBlackScholesVanillaEngine(bsmProcess, timeSteps, timeSteps - 1)
europeanOption.setPricingEngine(fdengine)
bermudanOption.setPricingEngine(fdengine)
americanOption.setPricingEngine(fdengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Jarrow-Rudd
method = 'Binomial Jarrow-Rudd'
jrengine = ql.BinomialJRVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(jrengine)
bermudanOption.setPricingEngine(jrengine)
americanOption.setPricingEngine(jrengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Cox-Ross-Rubinstein
method = 'Binomial Cox-Ross-Rubinstein'
crrengine = ql.BinomialCRRVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(crrengine)
bermudanOption.setPricingEngine(crrengine)
americanOption.setPricingEngine(crrengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Additive equiprobabilities
method = 'Additive equiprobabilities'
eqpengine = ql.BinomialEQPVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(eqpengine)
bermudanOption.setPricingEngine(eqpengine)
americanOption.setPricingEngine(eqpengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Binomial Trigeorgis
method = 'Binomial Trigeorgis'
trengine = ql.BinomialTrigeorgisVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(trengine)
bermudanOption.setPricingEngine(trengine)
americanOption.setPricingEngine(trengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Binomial Tian
method = 'Binomial Tian'
tiengine = ql.BinomialTianVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(tiengine)
bermudanOption.setPricingEngine(tiengine)
americanOption.setPricingEngine(tiengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Binomial Leisen-Reimer
method = 'Binomial Leisen-Reimer'
lrengine = ql.BinomialLRVanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(lrengine)
bermudanOption.setPricingEngine(lrengine)
americanOption.setPricingEngine(lrengine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
# Binomial method: Binomial Joshi
method = 'Binomial Joshi'
j4engine = ql.BinomialJ4VanillaEngine(bsmProcess, timeSteps)
europeanOption.setPricingEngine(j4engine)
bermudanOption.setPricingEngine(j4engine)
americanOption.setPricingEngine(j4engine)
tab.add_row([method, europeanOption.NPV(), bermudanOption.NPV(), americanOption.NPV()])
timeSteps = 1
# Monte Carlo Method: MC (crude)
method = 'MC (crude)'
mcSeed = 42
mcengine1 = ql.MakeMCPREuropeanEngine(bsmProcess)
mcengine1.withSteps(timeSteps)
mcengine1.withAbsoluteTolerance(0.02)
mcengine1.withSeed(mcSeed)
mcengine1 = mcengine1.makeEngine()
europeanOption.setPricingEngine(mcengine1)
tab.add_row([method, europeanOption.NPV(), 'N/A', 'N/A'])
# Monte Carlo Method: QMC (Sobol)
method = 'QMC (Sobol)'
nSamples = 32768 # 2^15
mcengine2 = ql.MakeMCLDEuropeanEngine(bsmProcess)
mcengine2.withSteps(timeSteps)
mcengine2.withSamples(nSamples)
mcengine2 = mcengine2.makeEngine()
europeanOption.setPricingEngine(mcengine2)
tab.add_row([method, europeanOption.NPV(), 'N/A', 'N/A'])
# Monte Carlo Method: MC (Longstaff Schwartz)
method = 'MC (Longstaff Schwartz)'
mcengine3 = ql.MakeMCPRAmericanEngine(bsmProcess)
mcengine3.withSteps(100)
mcengine3.withAntitheticVariate()
mcengine3.withCalibrationSamples(4096)
mcengine3.withAbsoluteTolerance(0.02)
mcengine3.withSeed(mcSeed)
mcengine3 = mcengine3.makeEngine()
americanOption.setPricingEngine(mcengine3)
tab.add_row([method, 'N/A', 'N/A', americanOption.NPV()])
tab.float_format = '.6'
tab.align = 'l'
print(tab)
'''
Option type = Put
Maturity = May 17th, 1999
Underlying price = 36
Strike = 40
Risk-free interest rate = 6.000000 %
Dividend yield = 0.000000 %
Volatility = 20.000000 %
Method European Bermudan American
Black-Scholes 3.844308 N/A N/A
Heston semi-analytic 3.844306 N/A N/A
Bates semi-analytic 3.844306 N/A N/A
Barone-Adesi/Whaley N/A N/A 4.459628
Bjerksund/Stensland N/A N/A 4.453064
Integral 3.844309 N/A N/A
Finite differences 3.844330 4.360765 4.486113
Binomial Jarrow-Rudd 3.844132 4.361174 4.486552
Binomial Cox-Ross-Rubinstein 3.843504 4.360861 4.486415
Additive equiprobabilities 3.836911 4.354455 4.480097
Binomial Trigeorgis 3.843557 4.360909 4.486461
Binomial Tian 3.844171 4.361176 4.486413
Binomial Leisen-Reimer 3.844308 4.360713 4.486076
Binomial Joshi 3.844308 4.360713 4.486076
MC (crude) 3.834522 N/A N/A
QMC (Sobol) 3.844613 N/A N/A
MC (Longstaff Schwartz) N/A N/A 4.456935
'''