Class MCAmericanBasketEngine

Namespace: NanoQL.PricingEngines

Assembly: NanoQL.dll

The Longstaff-Schwartz Monte Carlo engine for American and Bermudan basket options on correlated processes.

public static class MCAmericanBasketEngine

Inheritance: object

MCAmericanBasketEngine

Inherited Members: object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

The method is intrinsically weak for out-of-the-money options, as QuantLib warns. The pricing and the calibration draw from the same traits; the value, its error estimate where the traits allow one, and the exercise probability among the additional results as "exerciseProbability", as QuantLib's. The calibration is one call's working state.

The paths run on the clock spanning every Black-Scholes process's structures, each process read on it, and the payoffs are discounted on the first process's risk-free curve at that clock's times, where QuantLib evolves every process on the first's times (Divergences/TwoAssetMismatchedTimesTests.cs); a market on one clock keeps QuantLib's arithmetic.

Methods

Calculate<TRng, TStats>(BasketOption, EvaluationContext, StochasticProcessArray, int?, int?, bool, bool, int?, double?, int?, long, int?, int, LsmBasisSystemPolynomialType, long?)

Prices an American or Bermudan basket option by Longstaff-Schwartz.

public static MultiAssetOptionResults Calculate<TRng, TStats>(BasketOption option, EvaluationContext context, StochasticProcessArray processes, int? timeSteps, int? timeStepsPerYear, bool brownianBridge, bool antitheticVariate, int? requiredSamples, double? requiredTolerance, int? maxSamples, long seed, int? nCalibrationSamples = null, int polynomialOrder = 2, LsmBasisSystemPolynomialType polynomialType = LsmBasisSystemPolynomialType.Monomial, long? seedCalibration = null) where TRng : IRngTraits where TStats : IStatistics, new()

Parameters

option BasketOption: The basket option, of an early exercise.
context EvaluationContext: The evaluation context.
processes StochasticProcessArray: The assets' correlated processes, the first a Black-Scholes process.
timeSteps int?: The number of time steps, or null for steps per year.
timeStepsPerYear int?: The number of time steps per year, or null.
brownianBridge bool: Whether the draws are ordered by a Brownian bridge.
antitheticVariate bool: Whether antithetic variates are used.
requiredSamples int?: The number of samples, or null.
requiredTolerance double?: The absolute tolerance, or null.
maxSamples int?: The most samples for a tolerance, or null.
seed long: The seed, in [1, 4294967295].
nCalibrationSamples int?: The calibration samples, or null for 2,048.
polynomialOrder int: The regression basis' highest order.
polynomialType LsmBasisSystemPolynomialType: The regression basis' family.
seedCalibration long?: The calibration seed, in [1, 4294967295], or null for the Longstaff-Schwartz base's default; QuantLib's engine takes none, and its base's default is always 4294967295, the narrowed null, which passing that seed reproduces.

Returns

MultiAssetOptionResults: The option's results: the value, its error estimate, and the exercise probability.

Type Parameters

TRng: The random number traits of both simulations.
TStats: The statistics accumulator.

Exceptions

ArgumentNullException: An argument is null.
ArgumentException: The steps are given neither or both ways or aren't positive, or the basis family is another.
ArgumentOutOfRangeException: A number of samples is negative, or the seed is outside its range.
NanoQLException: The first process isn't a Black-Scholes process, the exercise isn't early or pays at expiry, or the samples can't reach the tolerance.

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