Class BetaRiskSimulation

Namespace

NanoQL.Experimental

Assembly

NanoQL.dll

The simulation of a BetaRisk: each path's events arrive as a Poisson process over the period, each event's loss the maximum loss times a beta draw, X / (X + Y) of two gamma draws.

[Experimental("NQL0001")]
[WorkingType]
public sealed class BetaRiskSimulation : CatSimulation

Inheritance

object

CatSimulation

BetaRiskSimulation

Inherited Members

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

The draws are those of QuantLib built with MSVC 14.44, its oracle's standard library: a 32-bit Mersenne Twister seeded with QuantLib's constant 5489, no parameter, as std::mt19937's default; each uniform from two of its integers as MSVC's generate_canonical forms it, the first's top 21 bits and the second's 32, (g₀ >> 11) + (g₁ << 21) times 2⁻⁵³, truncating where the standard's form rounds; the exponential as −log(1 − u)/λ; and the gamma by Knuth's published algorithms (TAOCP vol. 2, §3.4.1) in the order MSVC draws them: Ahrens-Dieter's GS below α = 1, the exponential at α = 1, a product of uniforms for an integer α below 20, and Ahrens' tangent method otherwise. They are written from those algorithms and this description of MSVC's behaviour; the standard leaves a distribution's algorithm to the implementation.

The event times are the inter-arrival times cumulated, so the count is Poisson's and a path's dates ascend: QuantLib's draws each event's time afresh, so its count is geometric, a mean of e^(λT) − 1 for λT (3.48 for 1.5 at a two-year return period over three years), and its dates come unordered, which the notional path reads as ascending. A path of one event or none is QuantLib's bit for bit up to the first path where QuantLib's next fresh draw falls inside the period and the cumulated time doesn't; the streams part there (Divergences/BetaRiskTests.cs).

A working type: each simulation owns its generator, stepping it in place.

Constructors

BetaRiskSimulation(Date, Date, double, double, double, double)

Initializes a new instance of the BetaRiskSimulation class.

public BetaRiskSimulation(Date start, Date end, double maxLoss, double lambda, double alpha, double beta)

Parameters

start Date

The period's start.

end Date

The period's end.

maxLoss double

The maximum loss.

lambda double

The events' rate, per year.

alpha double

The beta distribution's first parameter.

beta double

The beta distribution's second parameter.

Methods

GenerateBeta()

The next event's loss: the maximum loss times X / (X + Y), X and Y gamma draws of the beta distribution's parameters.

public double GenerateBeta()

Returns

double

The loss.

NextPath(List<KeyValuePair<Date, double>>)

Writes the next path's events into a list, cleared first.

public override bool NextPath(List<KeyValuePair<Date, double>> path)

Parameters

path List<KeyValuePair<Date, double>>

The list the events are written into.

Returns

bool

Whether a path was written; false when the simulation has run out of paths.