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"""
Copyright (C) 2024 Klaus Spanderen
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://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 unittest
import QuantLib as ql
class BasketOptionTest(unittest.TestCase):
def setUp(self):
self.todaysDate = ql.Date(26, ql.October, 2024)
ql.Settings.instance().evaluationDate = self.todaysDate
def tearDown(self):
ql.Settings.instance().evaluationDate = ql.Date()
def testThreeAssetSpreadOption(self):
"""Testing three asset spread option"""
def build_process(s: float, q: float, v: float) -> ql.BlackScholesMertonProcess:
return ql.BlackScholesMertonProcess(
ql.QuoteHandle(ql.SimpleQuote(s)),
ql.YieldTermStructureHandle(
ql.FlatForward(self.todaysDate, q, ql.Actual365Fixed())
),
ql.YieldTermStructureHandle(
ql.FlatForward(self.todaysDate, 0.05, ql.Actual365Fixed())
),
ql.BlackVolTermStructureHandle(
ql.BlackConstantVol(
self.todaysDate, ql.TARGET(), v, ql.Actual365Fixed()
)
),
)
processes = [
build_process(100, 0.05, 0.3),
build_process(50, 0.07, 0.45),
build_process(50, 0.025, 0.2),
]
processes_vector = ql.GeneralizedBlackScholesProcessVector(processes)
rho = ql.Matrix([[1.0, 0.2, -0.1], [0.2, 1.0, -0.3], [-0.1, -0.3, 1.0]])
exercise = ql.EuropeanExercise(self.todaysDate + ql.Period(1, ql.Years))
payoff = ql.PlainVanillaPayoff(ql.Option.Call, 2.0)
basket_option = ql.BasketOption(
ql.AverageBasketPayoff(payoff, ql.Array([1, -1, -1])), exercise
)
expected = 11.932739641
basket_option.setPricingEngine(ql.ChoiBasketEngine(processes_vector, rho, 10))
self.assertAlmostEqual(basket_option.NPV(), expected)
basket_option.setPricingEngine(ql.DengLiZhouBasketEngine(processes_vector, rho))
self.assertAlmostEqual(basket_option.NPV(), expected, 1)
basket_option.setPricingEngine(
ql.MCEuropeanBasketEngine(
ql.StochasticProcessArray(processes, rho),
"lowdiscrepancy",
timeSteps=1,
requiredTolerance=0.1,
)
)
self.assertAlmostEqual(basket_option.NPV(), expected, 1)
basket_option.setPricingEngine(
ql.FdndimBlackScholesVanillaEngine(
processes_vector, rho, ql.UnsignedIntVector([25, 15, 15]), 15
)
)
self.assertAlmostEqual(basket_option.NPV(), expected, 1)
def testTwoAssetSpreadOption(self):
"""Testing two asset spread option"""
def build_process(s: float, v: float) -> ql.BlackProcess:
return ql.BlackProcess(
ql.QuoteHandle(ql.SimpleQuote(s)),
ql.YieldTermStructureHandle(
ql.FlatForward(self.todaysDate, 0.05, ql.Actual365Fixed())
),
ql.BlackVolTermStructureHandle(
ql.BlackConstantVol(
self.todaysDate, ql.TARGET(), v, ql.Actual365Fixed()
)
),
)
p1 = build_process(100, 0.3)
p2 = build_process(90, 0.45)
rho = -0.75
rho_m = ql.Matrix([[1, rho], [rho, 1]])
processes_vector = ql.GeneralizedBlackScholesProcessVector([p1, p2])
exercise = ql.EuropeanExercise(self.todaysDate + ql.Period(6, ql.Months))
payoff = ql.PlainVanillaPayoff(ql.Option.Put, 10.0)
basket_option = ql.BasketOption(ql.SpreadBasketPayoff(payoff), exercise)
expected = 17.96241322097977
basket_option.setPricingEngine(ql.ChoiBasketEngine(processes_vector, rho_m, 15))
self.assertAlmostEqual(basket_option.NPV(), expected, 10)
basket_option.setPricingEngine(
ql.DengLiZhouBasketEngine(processes_vector, rho_m)
)
self.assertAlmostEqual(basket_option.NPV(), expected, 4)
basket_option.setPricingEngine(ql.KirkEngine(p1, p2, rho))
self.assertAlmostEqual(basket_option.NPV(), expected, 1)
basket_option.setPricingEngine(ql.BjerksundStenslandSpreadEngine(p1, p2, rho))
self.assertAlmostEqual(basket_option.NPV(), expected, 2)
basket_option.setPricingEngine(
ql.OperatorSplittingSpreadEngine(
p1, p2, rho, ql.OperatorSplittingSpreadEngine.First
)
)
self.assertAlmostEqual(basket_option.NPV(), expected, 1)
basket_option.setPricingEngine(
ql.OperatorSplittingSpreadEngine(
p1, p2, rho, ql.OperatorSplittingSpreadEngine.Second
)
)
self.assertAlmostEqual(basket_option.NPV(), expected, 2)
basket_option.setPricingEngine(
ql.FdndimBlackScholesVanillaEngine(
processes_vector, rho_m, ql.UnsignedIntVector([25, 25]), 15
)
)
self.assertAlmostEqual(basket_option.NPV(), expected, 1)
basket_option.setPricingEngine(
ql.Fd2dBlackScholesVanillaEngine(p1, p2, rho, xGrid=25, yGrid=25, tGrid=15)
)
self.assertAlmostEqual(basket_option.NPV(), expected, 1)
basket_option.setPricingEngine(
ql.MCEuropeanBasketEngine(
ql.StochasticProcessArray([p1, p2], rho_m),
"lowdiscrepancy",
timeSteps=1,
requiredTolerance=0.1,
)
)
self.assertAlmostEqual(basket_option.NPV(), expected, 1)
if __name__ == "__main__":
print("testing QuantLib", ql.__version__)
unittest.main(verbosity=2)
|
