import QuantLib as ql def option_price_european(S0, K, days_to_maturity, r, sigma, call=True, engine="BS", steps=200, paths=10000): # Pricing European options with different engines: Black-Scholes (BS), Binomial Tree (BT), and Monte Carlo (MC) today = ql.Date().todaysDate() maturity = today + days_to_maturity option_type = ql.Option.Call if call else ql.Option.Put payoff = ql.PlainVanillaPayoff(option_type, K) europeanExercise = ql.EuropeanExercise(maturity) europeanOption = ql.VanillaOption(payoff, europeanExercise) # Option parameters spot = ql.SimpleQuote(S0) riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, r, ql.Actual365Fixed())) volTS = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(today, ql.NullCalendar(), sigma, ql.Actual365Fixed())) process = ql.BlackScholesProcess(ql.QuoteHandle(spot), riskFreeTS, volTS) # Pricing engine selection if engine == "BS": engine = ql.AnalyticEuropeanEngine(process) elif engine == "BT": engine = ql.BinomialVanillaEngine(process, "crr", steps) elif engine == "MC": engine = ql.MCEuropeanEngine(process, "PseudoRandom", timeSteps=steps, requiredSamples=paths) europeanOption.setPricingEngine(engine) return europeanOption.NPV() def option_price_american(S0, K, days_to_maturity, r, sigma, call=True, steps=300): # Pricing American options using a binomial tree method today = ql.Date().todaysDate() maturity = today + days_to_maturity option_type = ql.Option.Call if call else ql.Option.Put payoff = ql.PlainVanillaPayoff(option_type, K) americanExercise = ql.AmericanExercise(today, maturity) americanOption = ql.VanillaOption(payoff, americanExercise) # Option parameters spot = ql.SimpleQuote(S0) riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, r, ql.Actual365Fixed())) volTS = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(today, ql.NullCalendar(), sigma, ql.Actual365Fixed())) process = ql.BlackScholesProcess(ql.QuoteHandle(spot), riskFreeTS, volTS) # Pricing with a binomial tree engine = ql.BinomialVanillaEngine(process, "crr", steps) americanOption.setPricingEngine(engine) return americanOption.NPV()

European vs. American Options: The Impact of Early Exercise on Pricing

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