Class OperatorSplittingSpreadEngine

Namespace

NanoQL.PricingEngines

Assembly

NanoQL.dll

The operator-splitting engine for a European spread option on two futures, to first or second order: Kirk's price with its corrections, from C. F. Lo, "Pricing Spread Options by the Operator Splitting Method", https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2429696.

public sealed class OperatorSplittingSpreadEngine : SpreadBlackScholesVanillaEngine

Inheritance

object

SpreadBlackScholesVanillaEngine

OperatorSplittingSpreadEngine

Inherited Members

SpreadBlackScholesVanillaEngine.Calculate(BasketOption, EvaluationContext)

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

Immutable. A put is priced from the call by parity.

A second forward and strike summing to zero or less is refused, where QuantLib takes the log of a negative number and returns NaN (Divergences/SpreadApproximationStrikeTests.cs); at a zero volatility of the second asset the corrections are their limit, 0, so the price is Kirk's, exact there, where QuantLib's are 0·∞ and the price NaN (Divergences/OperatorSplittingZeroVolatilityTests.cs).

Constructors

OperatorSplittingSpreadEngine(GeneralizedBlackScholesProcess, GeneralizedBlackScholesProcess, double, OperatorSplittingSpreadEngineOrder)

Initializes a new instance of the OperatorSplittingSpreadEngine class.

public OperatorSplittingSpreadEngine(GeneralizedBlackScholesProcess process1, GeneralizedBlackScholesProcess process2, double correlation, OperatorSplittingSpreadEngineOrder order = OperatorSplittingSpreadEngineOrder.Second)

Parameters

process1 GeneralizedBlackScholesProcess

The first asset's process.

process2 GeneralizedBlackScholesProcess

The second asset's process.

correlation double

The correlation of the two assets.

order OperatorSplittingSpreadEngineOrder

The approximation's order.

Exceptions

ArgumentNullException

A process is null.

ArgumentOutOfRangeException

order isn't one of its values.

Methods

Calculate(BasketOption, EvaluationContext, GeneralizedBlackScholesProcess, GeneralizedBlackScholesProcess, double, OperatorSplittingSpreadEngineOrder)

Prices a European spread option by operator splitting.

public static MultiAssetOptionResults Calculate(BasketOption option, EvaluationContext context, GeneralizedBlackScholesProcess process1, GeneralizedBlackScholesProcess process2, double correlation, OperatorSplittingSpreadEngineOrder order = OperatorSplittingSpreadEngineOrder.Second)

Parameters

option BasketOption

The option, on a SpreadBasketPayoff over a plain vanilla payoff.

context EvaluationContext

The evaluation context.

process1 GeneralizedBlackScholesProcess

The first asset's process.

process2 GeneralizedBlackScholesProcess

The second asset's process.

correlation double

The correlation of the two assets.

order OperatorSplittingSpreadEngineOrder

The approximation's order.

Returns

MultiAssetOptionResults

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

Exceptions

ArgumentNullException

An argument is null.

ArgumentOutOfRangeException

order isn't one of its values.

NanoQLException

The exercise isn't European, the payoff isn't a spread payoff over a plain vanilla payoff, or the second forward and the strike sum to zero or less.

Calculate(double, double, double, OptionType, double, double, double)

The value of a spread option on two forwards.

protected override double Calculate(double f1, double f2, double k, OptionType optionType, double variance1, double variance2, double df)

Parameters

f1 double

The first forward.

f2 double

The second forward.

k double

optionType OptionType

The option's type.

variance1 double

The first forward's Black variance to expiry.

variance2 double

The second forward's Black variance to expiry.

df double

The discount factor to expiry.

Returns

double

The value.