Class AnalyticDiscreteGeometricAveragePriceAsianEngine

Namespace

NanoQL.PricingEngines

Assembly

NanoQL.dll

The analytic engine for discrete geometric average-price Asian options: the geometric average of log-normal fixings is log-normal, priced by Black's formula on its forward and variance (Clewlow and Strickland, "Implementing Derivatives Models", 1998, pp. 118-123).

public static class AnalyticDiscreteGeometricAveragePriceAsianEngine

Inheritance

object

AnalyticDiscreteGeometricAveragePriceAsianEngine

Inherited Members

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

The value and the Greeks QuantLib sets. It also prices an arithmetic option, as the geometric control of the arithmetic Monte Carlo engine, reading no past fixing, as QuantLib's does.

Documented divergences. The average is priced exactly under deterministic term structures: ln G is normal with mean (1/N)(the past fixings' log-sum + Σ[ln F(tᵢ) − V(tᵢ)/2]) and variance (1/N²)ΣΣV(min(tᵢ, tⱼ)) over the future fixings, F the forward and V the Black variance at the strike, each read by date, where QuantLib reads one volatility at the exercise date and the zero rates to it for every fixing, +37.4% and −18.9% off on shaped markets (Divergences/GeometricAsianTermStructureTests.cs). The Greeks are the form's: vega under a parallel shift of the volatilities, rho and dividend rho under parallel shifts of the curves, each on its own structure's clock; on a flat market they are QuantLib's. A running product that has left double's range is read through the past fixings' log-sum, where QuantLib prices ∞ (Divergences/GeometricAsianProductRangeTests.cs).

A fixing dated from the evaluation date to the clock's origin, where the structures settle after the evaluation date, is taken at the origin, the spot with no variance and no discount accrued, so as a past fixing at the spot (Divergences/AsianLateSettlementTests.cs), where QuantLib drops it from the average.

Methods

Calculate(DiscreteAveragingAsianOption, EvaluationContext, GeneralizedBlackScholesProcess)

Prices a discrete geometric average-price Asian option.

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

Parameters

option DiscreteAveragingAsianOption

The option.

context EvaluationContext

The evaluation context.

process GeneralizedBlackScholesProcess

The Black-Scholes process.

Returns

OneAssetOptionResults

The option's results: the value, delta, gamma, vega, rho, dividend rho, theta and strike sensitivity; the expired results when the option has expired.

Exceptions

ArgumentNullException

An argument is null.

NanoQLException

The exercise isn't European, the payoff isn't plain vanilla, the spot isn't positive, or the option's past fixings fail its checks.