Table of Contents

Class MCLongstaffSchwartzEngine<TOption, TMc, TMcCalibration, TPath, TState, TStats>

Namespace
NanoQL.PricingEngines
Assembly
NanoQL.dll

The Longstaff-Schwartz Monte Carlo engine for early-exercise options (Francis Longstaff, Eduardo Schwartz, 2001, "Valuing American Options by Simulation: A Simple Least-Squares Approach", The Review of Financial Studies, Volume 14, No. 1, 113-147): a calibration simulation whose paths the Longstaff-Schwartz pricer regresses, then the pricing simulation on the same pricer.

public abstract class MCLongstaffSchwartzEngine<TOption, TMc, TMcCalibration, TPath, TState, TStats> : McSimulation<TPath, TStats> where TOption : Option where TMc : IMcTraits<TPath> where TMcCalibration : IMcTraits<TPath> where TStats : IStatistics, new()

Type Parameters

TOption

The option, QuantLib's GenericEngine's instrument.

TMc

The pricing simulation's Monte Carlo traits, QuantLib's MC<RNG>.

TMcCalibration

The calibration's traits, QuantLib's MC<RNG_Calibration>.

TPath

The path type.

TState

The early-exercise pricer's state type, which QuantLib's traits name for the path type.

TStats

The statistics accumulator.

Inheritance
McSimulation<TPath, TStats>
MCLongstaffSchwartzEngine<TOption, TMc, TMcCalibration, TPath, TState, TStats>
Inherited Members

Remarks

An extension point and an immutable object: a concrete engine's static Calculate builds one per call and implements LsmPathPricer(). Run() builds the pricer, adds the calibration samples on the calibration traits' generator, calibrates, prices on the same pricer and returns the model with the call's exercise probability: QuantLib's mutable pricer and calibration model are the call's working state, and the pricer reaches the pricing model as the call's argument, not as a member, so two calls can share one engine object.

The calibration samples default to 2,048, and the calibration's Brownian bridge and antithetic variates to the pricing's. The calibration seed defaults to the pricing seed plus 1,768,237,423, modulo 2³² as MSVC's 32-bit unsigned long computes it, as QuantLib's documentation says; QuantLib's code compares the narrowed Null<Size>() with Null<Real>(), so its default is always the narrowed null: a documented divergence (Divergences/LongstaffSchwartzCalibrationSeedTests.cs); QuantLib's engine with that seed passed reproduces this one's default. Where that default is 0, at the pricing seed 2,526,729,873, it is refused, since QuantLib reads 0 as a seed from the clock.

The pricer exercises only at the exercise times on the grid (ExerciseTimes(TimeGrid)): a Bermudan option's dates, and an American option's grid times from its earliest exercise.

Constructors

MCLongstaffSchwartzEngine(TOption, EvaluationContext, StochasticProcess, int?, int?, bool, bool, bool, int?, double?, int?, long, int?, bool?, bool?, long?)

Initializes a new instance of the MCLongstaffSchwartzEngine<TOption, TMc, TMcCalibration, TPath, TState, TStats> class.

protected MCLongstaffSchwartzEngine(TOption option, EvaluationContext context, StochasticProcess process, int? timeSteps, int? timeStepsPerYear, bool brownianBridge, bool antitheticVariate, bool controlVariate, int? requiredSamples, double? requiredTolerance, int? maxSamples, long seed, int? nCalibrationSamples = null, bool? brownianBridgeCalibration = null, bool? antitheticVariateCalibration = null, long? seedCalibration = null)

Parameters

option TOption

The option.

context EvaluationContext

The evaluation context.

process StochasticProcess

The process the paths follow.

timeSteps int?

The number of time steps, or null for steps per year.

timeStepsPerYear int?

The number of time steps per year, or null for a number of steps.

brownianBridge bool

Whether the pricing draws are ordered by a Brownian bridge.

antitheticVariate bool

Whether the pricing uses antithetic variates.

controlVariate bool

Whether a control variate is used.

requiredSamples int?

The number of samples, or null.

requiredTolerance double?

The absolute tolerance, or null; it takes precedence.

maxSamples int?

The most samples for a tolerance, or null for no limit.

seed long

The pricing seed, in [1, 4294967295].

nCalibrationSamples int?

The calibration samples, or null for 2,048.

brownianBridgeCalibration bool?

The calibration's Brownian bridge, or null for the pricing's.

antitheticVariateCalibration bool?

The calibration's antithetic variates, or null for the pricing's.

seedCalibration long?

The calibration seed, in [1, 4294967295], or null for (seed + 1768237423) mod 2³².

Exceptions

ArgumentNullException

The option, the context or the process is null.

ArgumentException

Neither or both of the time steps and the time steps per year are given, or the one given isn't positive.

ArgumentOutOfRangeException

A number of samples is negative, a seed is outside its range, or the default calibration seed is 0.

Properties

AntitheticVariateCalibration

Gets a value indicating whether the calibration uses antithetic variates.

protected bool AntitheticVariateCalibration { get; }

Property Value

bool

BrownianBridge

Gets a value indicating whether the pricing draws are ordered by a Brownian bridge.

protected bool BrownianBridge { get; }

Property Value

bool

BrownianBridgeCalibration

Gets a value indicating whether the calibration draws are ordered by a Brownian bridge.

protected bool BrownianBridgeCalibration { get; }

Property Value

bool

Context

Gets the evaluation context.

protected EvaluationContext Context { get; }

Property Value

EvaluationContext

MaxSamples

Gets the most samples for a tolerance, or null for no limit.

protected int? MaxSamples { get; }

Property Value

int?

NCalibrationSamples

Gets the number of calibration samples.

protected int NCalibrationSamples { get; }

Property Value

int

Option

Gets the option, QuantLib's engine arguments.

protected TOption Option { get; }

Property Value

TOption

Process

Gets the process the paths follow.

protected StochasticProcess Process { get; }

Property Value

StochasticProcess

RequiredSamples

Gets the number of samples, or null.

protected int? RequiredSamples { get; }

Property Value

int?

RequiredTolerance

Gets the absolute tolerance, or null.

protected double? RequiredTolerance { get; }

Property Value

double?

Seed

Gets the pricing seed.

protected long Seed { get; }

Property Value

long

SeedCalibration

Gets the calibration seed.

protected long SeedCalibration { get; }

Property Value

long

TimeSteps

Gets the number of time steps, or null.

protected int? TimeSteps { get; }

Property Value

int?

TimeStepsPerYear

Gets the number of time steps per year, or null.

protected int? TimeStepsPerYear { get; }

Property Value

int?

Methods

ExerciseTimes(TimeGrid)

The grid's exercise times, beside its last, for the Longstaff-Schwartz pricer: a Bermudan option's exercise times after the start, and an American option's grid times from its earliest exercise.

protected IReadOnlyList<double> ExerciseTimes(TimeGrid grid)

Parameters

grid TimeGrid

The grid.

Returns

IReadOnlyList<double>

The times.

LsmPathPricer()

The Longstaff-Schwartz pricer of this call, new.

protected abstract LongstaffSchwartzPathPricer<TPath, TState> LsmPathPricer()

Returns

LongstaffSchwartzPathPricer<TPath, TState>

The pricer.

PathGenerator()

The pricing simulation's path generator: the traits' generator of the process's factors per step.

protected override IPathGenerator<TPath> PathGenerator()

Returns

IPathGenerator<TPath>

A new path generator.

PathPricer()

QuantLib's pathPricer(), which returns the pricer its calculate stored: Run() passes the call's calibrated pricer to the pricing model, so outside it there is none.

protected override PathPricer<TPath> PathPricer()

Returns

PathPricer<TPath>

Nothing: it throws.

Exceptions

NanoQLException

Always ("path pricer unknown").

Run()

QuantLib's calculate: the calibration simulation, the regression and the pricing simulation on the same Longstaff-Schwartz pricer.

protected (MonteCarloModel<TPath, TStats> Model, double ExerciseProbability) Run()

Returns

(MonteCarloModel<TPath, TStats> Model, double ExerciseProbability)

The pricing model and the call's exercise probability.

Exceptions

NanoQLException

The simulation refuses, or the samples can't reach the tolerance.

TimeGrid()

The time grid: to an American option's last exercise, or through a Bermudan's exercise times after the start, in the steps given or the steps per year of the last time, at least one.

protected override TimeGrid TimeGrid()

Returns

TimeGrid

The grid.

Exceptions

NanoQLException

No exercise time lies after the start, or no steps are given.