My goal is to price American basket put options using the Least squares Monte Carlo, or Longstaff-Schwartz algorithm.
I currently have the one-dimensional case working with the Python file below (I am using the SWIG package), but I would like to change the number of basis functions used by the AmericanBasketEngine to make sure the price is accurate. How do I do this?
Looking at the C++ source, I found the polynomOrder keyword argument with default value 2 of the class AmericanBasketPathPricer. However, I do not know how this class is connected to the MCAmericanBasketEngine, which does not have such a keyword argument. (I never programmed in either C or C++, so I am quite lost in the source.)
Maybe is the polynomial order determined automatically, based on the requiredTolerance? That would be ideal, but I couldn't find a description of what the MCAmericanBasketEngine does exactly anywhere.
from QuantLib import *
d=1 #To be increased...
todaysDate = Date(15,May,1998)
Settings.instance().evaluationDate = todaysDate
settlementDate = Date(17,May,1998)
riskFreeRate = FlatForward(settlementDate, 0.05, Actual365Fixed())
payoff = PlainVanillaPayoff(Option.Put, 100.0)
underlying1 = SimpleQuote(100.0)
volatility1 = BlackConstantVol(todaysDate, TARGET(), 0.30, Actual365Fixed())
dividendYield1 = FlatForward(settlementDate, 0.00, Actual365Fixed())
process1 = BlackScholesMertonProcess(QuoteHandle(underlying1),
YieldTermStructureHandle(dividendYield1),
YieldTermStructureHandle(riskFreeRate),
BlackVolTermStructureHandle(volatility1))
procs = StochasticProcessVector()
procs.push_back(process1)
matrix = Matrix(1,1)
matrix[0][0] = 1.0
process = StochasticProcessArray(procs, matrix)
american_exercise = AmericanExercise(Date(17,May,1998),Date(17,May,1999))
basketoption = BasketOption(AverageBasketPayoff(payoff,d),american_exercise)
basketoption.setPricingEngine(
MCAmericanBasketEngine(
process,
'pseudorandom',
polynomOrder = 2,#keyword does not exist
timeStepsPerYear = 100,
requiredTolerance = 0.01,
#seed = 42))
)
)
print(basketoption.NPV())
