Class AnalyticContinuousFixedLookbackEngine

Namespace

NanoQL.PricingEngines

Assembly

NanoQL.dll

The analytic engine for continuous fixed-strike lookback options: Conze and Viswanathan's closed form, as in Haug, "Option Pricing Formulas" (1998), pp. 63-64.

public static class AnalyticContinuousFixedLookbackEngine

Inheritance

object

AnalyticContinuousFixedLookbackEngine

Inherited Members

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

The value alone, as QuantLib's. At zero carry, where the formula's ratio is 0/0, its limit, upstream's fix after v1.44 (#2856).

Documented divergences. Each rate is read on the volatility's clock and each time is the volatility's, as AnalyticBarrierEngine reads them, where QuantLib reads every structure at the risk-free curve's times (Divergences/LookbackMismatchedTimesTests.cs). The extremum observed so far is read as the spot where it lies beyond it, the spot being observed, where QuantLib prices the impossible extremum (Divergences/LookbackExtremeBeyondSpotTests.cs). Near zero carry the formula is evaluated in double-double, where QuantLib's double cancels and #2856 switches to its limit below |λ| of 1e-7 (NanoQL.PricingEngines.LookbackSmallCarry, Divergences/LookbackSmallCarryTests.cs). At small volatilities, where λ = 2b/σ² is large and QuantLib's power of s times its normal factor is +∞ times 0, NaN, the product is taken in logs (NanoQL.PricingEngines.LookbackTails, Divergences/LookbackSmallVolatilityTests.cs). And below machine-epsilon variance the underlying follows its forward, where QuantLib divides by the volatility (Divergences/LookbackZeroVolatilityTests.cs).

The formula is a first-passage closed form in equivalent-constant rates and a volatility, the variance and discounts to expiry: no exact closed form exists for a first passage under general deterministic term structures; the term-structure-exact route is MCLookbackEngine.

Methods

Calculate(ContinuousFixedLookbackOption, EvaluationContext, GeneralizedBlackScholesProcess)

Prices a continuous fixed-strike lookback option.

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

Parameters

option ContinuousFixedLookbackOption

The option, not a partial-time one.

context EvaluationContext

The evaluation context.

process GeneralizedBlackScholesProcess

The Black-Scholes process.

Returns

OneAssetOptionResults

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

Exceptions

ArgumentNullException

An argument is null.

NanoQLException

The option is a ContinuousPartialFixedLookbackOption ("wrong argument type", QuantLib's refusal of its arguments), its extremum is negative, its payoff isn't plain vanilla, the spot isn't positive, or the strike is negative (a call) or not positive (a put).