template class xf::fintech::internal::HJMPcaEngine

#include "hjm_engine.hpp"

Overview

Class for calculating the inputs to the MonteCarlo simulation of Heath-Jarrow-Morton framework. It deals with analysing historical data, calculating the risk neutral drift and the polynomial fitting of the discrete volatility vectors.

Parameters:

DT	DataType for the internal calculations
MAX_TENORS	Maximum synthetisable tenors supported by the framework.
MAX_CURVES	Maximum number of days analyzable from historical data
NCU	Number of compute units on the historical data matrix.

template <
    typename DT,
    unsigned int MAX_TENORS,
    unsigned MAX_CURVES,
    unsigned NCU
    >
class HJMPcaEngine: public hjmModelParams

Methods

riskNeutralDrift

void riskNeutralDrift (
    DT vol_c1] [PD[0],
    DT vol_c2] [PD[1],
    DT vol_c3] [PD[2],
    DT rnd [MAX_TENORS]
    )

Risk Neutral drift calculation. tau assumed to be 0.5 years.

RnD calculated as :math:` vol(t) * integral(vol(t)) ` for all volatilities and for :math:` t=1,…,n `

volatility_polyfit

void volatility_polyfit (
    DT discreteVols [MAX_TENORS][N],
    DT vol1] [VOL_POLYFIT_FANOUT][PD[0],
    DT vol2] [VOL_POLYFIT_FANOUT][PD[1],
    DT vol3] [VOL_POLYFIT_FANOUT][PD[2]
    )

Transforms each discrete volatility vector into a continuous least-squares fitting of a polynomial. The chosen degrees for the polynomial is a model specific parameter selected for better convergence. Each set of coefficients is also split into several copies for its use in different parts of the model. The outputs is a set of coefficients, ‘degree + 1’ elements wide that represent the function :math:` c_0 + c_1*x + c_2*x^2 + … + c_n*x^n ` .

Parameters:

discreteVols	Matrix with discrete volatilities arranged in sets of N vectors.
vol1	Polynomial coefficients for the first volatility vector
vol2	Polynomial coefficients for the second volatility vector
vol3	Polynomial coefficients for the third volatility vector

matdiffRows

template <
    unsigned R,
    unsigned C
    >
void matdiffRows (
    DT input [R][C],
    DT output [R-1][C],
    unsigned r,
    unsigned c
    )

matdiff function that computes the difference between rows in a matrix.

Parameters:

input	Input matrix data.
output	Output containing the diff of the matrix data. It will contain 1 fewer row than the original.

mtransp

template <
    unsigned R,
    unsigned C
    >
void mtransp (
    unsigned r,
    unsigned c,
    DT input [R][C],
    DT output [C][R]
    )

Calculates the transpose of a matrix.

calculateDiscreteVolatility

void calculateDiscreteVolatility (
    DT ratesIn [MAX_CURVES][MAX_TENORS],
    DT discreteVols [MAX_TENORS][N]
    )

Extracts N discrete volatility vectors from a matrix of historical interest rates. A Principal Component Analysis will be performed on the differences of the data, and a dimensionality reduction will be performed to extract the noTenors datapoints for each vector.

Parameters:

ratesIn	Matrix with all the raw historical data, with size noTenors x noObservations
discreteVols	Output vectors of the discrete volatilities arranged in sets of N. It will contain noTenors elements.