R1ProbabilityDensityFunctionCIR.java
package org.drip.dynamics.process;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>R1ProbabilityDensityFunctionCIR</i> exposes the R<sup>1</sup> Probability Density Function Evaluation
* Equation for an Underlying CIR Process. The References are:
*
* <br><br>
* <ul>
* <li>
* Bogoliubov, N. N., and D. P. Sankevich (1994): N. N. Bogoliubov and Statistical Mechanics
* <i>Russian Mathematical Surveys</i> <b>49 (5)</b> 19-49
* </li>
* <li>
* Holubec, V., K. Kroy, and S. Steffenoni (2019): Physically Consistent Numerical Solver for
* Time-dependent Fokker-Planck Equations <i>Physical Review E</i> <b>99 (4)</b> 032117
* </li>
* <li>
* Kadanoff, L. P. (2000): <i>Statistical Physics: Statics, Dynamics, and Re-normalization</i>
* <b>World Scientific</b>
* </li>
* <li>
* Ottinger, H. C. (1996): <i>Stochastic Processes in Polymeric Fluids</i> <b>Springer-Verlag</b>
* Berlin-Heidelberg
* </li>
* <li>
* Wikipedia (2019): Fokker-Planck Equation
* https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/README.md">HJM, Hull White, LMM, and SABR Dynamic Evolution Models</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/process/README.md">Ito-Dynamics Based Stochastic Process</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class R1ProbabilityDensityFunctionCIR
extends org.drip.dynamics.process.R1ProbabilityDensityFunction
{
private double _q = java.lang.Double.NaN;
private double _r0 = java.lang.Double.NaN;
private double _twoAOverSigmaSquared = java.lang.Double.NaN;
private org.drip.dynamics.meanreverting.CKLSParameters _cklsParameters = null;
private org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
_modifiedBesselFirstKindEstimator = null;
/**
* R1ProbabilityDensityFunctionCIR Constructor
*
* @param r0 Starting Value for r
* @param cklsParameters The CKLS Parameters
* @param modifiedBesselFirstKindEstimator Modified Bessel Estimator of the First Kind
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public R1ProbabilityDensityFunctionCIR (
final double r0,
final org.drip.dynamics.meanreverting.CKLSParameters cklsParameters,
final org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
modifiedBesselFirstKindEstimator)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
_r0 = r0
) ||
null == (_cklsParameters = cklsParameters) ||
null == (_modifiedBesselFirstKindEstimator = modifiedBesselFirstKindEstimator)
)
{
throw new java.lang.Exception (
"R1ProbabilityDensityFunctionCIR Constructor => Invalid Inputs"
);
}
double volatilityCoefficient = _cklsParameters.volatilityCoefficient();
_q = _cklsParameters.meanReversionLevel() * (
_twoAOverSigmaSquared = 2. * _cklsParameters.meanReversionSpeed() / volatilityCoefficient /
volatilityCoefficient
) - 1.;
}
/**
* Retrieve "q"
*
* @return "q"
*/
public double q()
{
return _q;
}
/**
* Retrieve the Starting Value for r
*
* @return Starting Value for r
*/
public double r0()
{
return _r0;
}
/**
* Retrieve the CKLS Parameters
*
* @return The CKLS Parameters
*/
public org.drip.dynamics.meanreverting.CKLSParameters cklsParameters()
{
return _cklsParameters;
}
/**
* Retrieve the Modified Bessel Estimator of the First Kind
*
* @return The Modified Bessel Estimator of the First Kind
*/
public org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
modifiedBesselFirstKindEstimator()
{
return _modifiedBesselFirstKindEstimator;
}
@Override public double density (
final org.drip.dynamics.ito.TimeR1Vertex r1TimeVertex)
throws java.lang.Exception
{
if (null == r1TimeVertex)
{
throw new java.lang.Exception (
"R1ProbabilityDensityFunctionCIR::density => Invalid Inputs"
);
}
double ePowerMinusAT = java.lang.Math.exp (
-1. * _cklsParameters.meanReversionSpeed() * r1TimeVertex.t()
);
double c = _twoAOverSigmaSquared / (1. - ePowerMinusAT);
double u = c * _r0 * ePowerMinusAT;
double v = c * r1TimeVertex.x();
return c * java.lang.Math.exp (
-1. * (u + v)
) * java.lang.Math.pow (
u / v,
0.5 * _q
) * _modifiedBesselFirstKindEstimator.bigI (
_q,
2. * java.lang.Math.sqrt (
u * v
)
);
}
}