Class FdCEVVanillaEngine

Namespace: NanoQL.PricingEngines

Assembly: NanoQL.dll

The finite-difference pricing engine for vanilla options, European, American or Bermudan, on the constant elasticity of variance (CEV) process df = α·f^β·dW, absorbed at f = 0: on FdmCEV1dMesher's grid, concentrating at the strike, with the analytic CEV value at the upper end and, where the process can reach zero (δ < 2), the payoff at the lower end discounted from maturity.

public static class FdCEVVanillaEngine

Inheritance: object

FdCEVVanillaEngine

Inherited Members: object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

The engine reports the value, delta, gamma and theta; the theta is null when the problem's first stopping time is time 0, as QuantLib's is. Its finite-difference working types are built inside each calculation and dropped after it. Its times are the discount curve's, from its reference date in its day counter, as QuantLib's; an exercise on or before that date leaves the engine no time to roll back over, and it is refused, as QuantLib's engine throws there (Boost's refusal of an infinite non-centrality, or a negative time in the incomplete gamma function), and as nanoql's other finite-difference engines refuse an exercise their clocks have no time for.

Near β = 1 the mesher's bounds and the upper end's value are the lognormal limit's and Black's formula at Hagan's equivalent volatility (FdmCEV1dMesher, CEVCalculator), where QuantLib's engine throws.

Methods

Calculate(VanillaOption, EvaluationContext, double, double, double, YieldTermStructure, int, int, int, double, double, FdmSchemeDesc?)

Prices a vanilla option.

public static OneAssetOptionResults Calculate(VanillaOption option, EvaluationContext context, double f0, double alpha, double beta, YieldTermStructure discountCurve, int tGrid = 50, int xGrid = 400, int dampingSteps = 0, double scalingFactor = 1, double eps = 0.0001, FdmSchemeDesc? schemeDesc = null)

Parameters

option VanillaOption: The option.
context EvaluationContext: The evaluation context.
f0 double: The forward's value today.
alpha double: The volatility parameter α.
beta double: The elasticity β.
discountCurve YieldTermStructure: The discount curve.
tGrid int: The number of time steps.
xGrid int: The number of the forward's points.
dampingSteps int: The number of implicit damping steps.
scalingFactor double: The factor the mesher's ends are widened by.
eps double: The probability outside each end of the mesher.
schemeDesc FdmSchemeDesc?: The scheme; null for Douglas, QuantLib's default.

Returns

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

Exceptions

ArgumentNullException: The option, the context or the curve is null.
ArgumentOutOfRangeException: A grid size or the damping steps is negative.
ArgumentException: The exercise is on or before the curve's reference date, or the grid is too small.
NanoQLException: The payoff isn't striked, or the density, the analytic value or the solver refuses its arguments.