Class BaroneAdesiWhaleyApproximationEngine

Namespace

NanoQL.PricingEngines

Assembly

NanoQL.dll

The Barone-Adesi and Whaley pricing engine for American options (1987).

public static class BaroneAdesiWhaleyApproximationEngine

Inheritance

object

BaroneAdesiWhaleyApproximationEngine

Inherited Members

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

The correctness of the returned value is tested by reproducing results available in literature. Where early exercise is never optimal the engine reports the European value and every Greek; otherwise the value alone.

The critical price's Newton step can leave (0, K) for a put, or (K, ∞) for a call, and the next Black formula then throws (baroneadesiwhaleyengine.cpp:83-130); so does a call's seed where h > 0 takes it below zero (:59-64, then the Black formula of :93). Here the critical price is then the root of QuantLib's own equation over that range, by Brent's method. Every case where Newton stays in range keeps QuantLib's bits (Divergences/BaroneAdesiWhaleyCriticalPriceTests.cs).

Each structure is read at the exercise date by date, nothing accrued before its own reference date; where early exercise is never optimal the theta's terms run over each structure's own time, as the analytic European engine's, where QuantLib's run over the volatility's (Divergences/ApproximationThetaMismatchedTimesTests.cs). An exercise window opening after the reference date is priced by NanoQL.PricingEngines.ApproximationWindow, where QuantLib reads the last date alone (Divergences/ApproximationWindowTests.cs).

Methods

Calculate(VanillaOption, EvaluationContext, GeneralizedBlackScholesProcess)

Prices an American vanilla option.

public static OneAssetOptionResults Calculate(VanillaOption option, EvaluationContext context, GeneralizedBlackScholesProcess process)

Parameters

option VanillaOption

The option.

context EvaluationContext

The evaluation context.

process GeneralizedBlackScholesProcess

The Black-Scholes process.

Returns

OneAssetOptionResults

The option's results; the expired results when it has expired.

Exceptions

ArgumentNullException

An argument is null.

NanoQLException

The exercise isn't American or pays at expiry, the payoff isn't striked, the underlying isn't positive, or the critical price refuses.

CriticalPrice(StrikedTypePayoff, double, double, double, double)

The critical commodity price: the underlying's level at which early exercise becomes optimal.

public static double CriticalPrice(StrikedTypePayoff payoff, double riskFreeDiscount, double dividendDiscount, double variance, double tolerance = 1E-06)

Parameters

payoff StrikedTypePayoff

The payoff.

riskFreeDiscount double

The risk-free discount to expiry, at most 1.

dividendDiscount double

The dividend discount to expiry.

variance double

The Black variance to expiry.

tolerance double

The tolerance on QuantLib's equation, relative to the strike.

Returns

double

The critical price.

Exceptions

ArgumentNullException

payoff is null.

NanoQLException

The risk-free discount is above 1, or the option type is unknown.