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# ---
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# ---
# # Basket options
#
# Copyright (©) 2004, 2005, 2006 StatPro Italia srl
#
# This file is part of QuantLib, a free-software/open-source library
# for financial quantitative analysts and developers - https://www.quantlib.org/
#
# QuantLib is free software: you can redistribute it and/or modify it under the
# terms of the QuantLib license. You should have received a copy of the
# license along with this program; if not, please email
# <quantlib-dev@lists.sf.net>. The license is also available online at
# <https://www.quantlib.org/license.shtml>.
#
# This program is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the license for more details.
import QuantLib as ql
# ### Global data
todaysDate = ql.Date(15, ql.May, 1998)
ql.Settings.instance().evaluationDate = todaysDate
settlementDate = ql.Date(17, ql.May, 1998)
riskFreeRate = ql.FlatForward(settlementDate, 0.05, ql.Actual365Fixed())
# ### Option parameters
exercise = ql.EuropeanExercise(ql.Date(17, ql.May, 1999))
payoff = ql.PlainVanillaPayoff(ql.Option.Call, 8.0)
# ### Market data
underlying1 = ql.SimpleQuote(7.0)
volatility1 = ql.BlackConstantVol(todaysDate, ql.TARGET(), 0.10, ql.Actual365Fixed())
dividendYield1 = ql.FlatForward(settlementDate, 0.05, ql.Actual365Fixed())
underlying2 = ql.SimpleQuote(7.0)
volatility2 = ql.BlackConstantVol(todaysDate, ql.TARGET(), 0.10, ql.Actual365Fixed())
dividendYield2 = ql.FlatForward(settlementDate, 0.05, ql.Actual365Fixed())
process1 = ql.BlackScholesMertonProcess(
ql.QuoteHandle(underlying1),
ql.YieldTermStructureHandle(dividendYield1),
ql.YieldTermStructureHandle(riskFreeRate),
ql.BlackVolTermStructureHandle(volatility1),
)
process2 = ql.BlackScholesMertonProcess(
ql.QuoteHandle(underlying2),
ql.YieldTermStructureHandle(dividendYield2),
ql.YieldTermStructureHandle(riskFreeRate),
ql.BlackVolTermStructureHandle(volatility2),
)
matrix = ql.Matrix(2, 2)
matrix[0][0] = 1.0
matrix[1][1] = 1.0
matrix[0][1] = 0.5
matrix[1][0] = 0.5
process = ql.StochasticProcessArray([process1, process2], matrix)
# ### Pricing
basketoption = ql.BasketOption(ql.MaxBasketPayoff(payoff), exercise)
basketoption.setPricingEngine(
ql.MCEuropeanBasketEngine(process, "pseudorandom", timeStepsPerYear=1, requiredTolerance=0.02, seed=42)
)
print("Maximum Basket Payoff: ", basketoption.NPV())
basketoption = ql.BasketOption(ql.MinBasketPayoff(payoff), exercise)
basketoption.setPricingEngine(
ql.MCEuropeanBasketEngine(process, "pseudorandom", timeStepsPerYear=1, requiredTolerance=0.02, seed=42)
)
print("Minimum Basket Payoff: ", basketoption.NPV())
basketoption = ql.BasketOption(ql.AverageBasketPayoff(payoff, 2), exercise)
basketoption.setPricingEngine(
ql.MCEuropeanBasketEngine(process, "pseudorandom", timeStepsPerYear=1, requiredTolerance=0.02, seed=42)
)
print("Average Basket Payoff: ", basketoption.NPV())
americanExercise = ql.AmericanExercise(settlementDate, ql.Date(17, ql.May, 1999))
americanbasketoption = ql.BasketOption(ql.MaxBasketPayoff(payoff), americanExercise)
americanbasketoption.setPricingEngine(
ql.MCAmericanBasketEngine(
process,
"pseudorandom",
timeSteps=10,
requiredTolerance=0.02,
seed=42,
polynomOrder=5,
polynomType=ql.LsmBasisSystem.Hermite,
)
)
print("Basket American Exercise: ", americanbasketoption.NPV())
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