R1CIRStochasticEvolver.java
package org.drip.dynamics.meanreverting;
/*
* -*- 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>R1CIRStochasticEvolver</i> implements the R<sup>1</sup> Cos-Ingersoll-Ross Stochastic Evolver. The
* References are:
*
* <br><br>
* <ul>
* <li>
* Doob, J. L. (1942): The Brownian Movement and Stochastic Equations <i>Annals of Mathematics</i>
* <b>43 (2)</b> 351-369
* </li>
* <li>
* Gardiner, C. W. (2009): <i>Stochastic Methods: A Handbook for the Natural and Social Sciences
* 4<sup>th</sup> Edition</i> <b>Springer-Verlag</b>
* </li>
* <li>
* Kadanoff, L. P. (2000): <i>Statistical Physics: Statics, Dynamics, and Re-normalization</i>
* <b>World Scientific</b>
* </li>
* <li>
* Karatzas, I., and S. E. Shreve (1991): <i>Brownian Motion and Stochastic Calculus 2<sup>nd</sup>
* Edition</i> <b>Springer-Verlag</b>
* </li>
* <li>
* Risken, H., and F. Till (1996): <i>The Fokker-Planck Equation – Methods of Solution and
* Applications</i> <b>Springer</b>
* </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/meanreverting/README.md">Mean Reverting Stochastic Process Dynamics</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class R1CIRStochasticEvolver
extends org.drip.dynamics.meanreverting.R1CKLSStochasticEvolver
{
/**
* Construct a Weiner Instance of R1CIRStochasticEvolver Process
*
* @param meanReversionSpeed The Mean Reversion Speed
* @param meanReversionLevel The Mean Reversion Level
* @param volatility The Volatility
* @param timeWidth Wiener Time Width
*
* @return Weiner Instance of R1CIRStochasticEvolver Process
*/
public static R1CIRStochasticEvolver Wiener (
final double meanReversionSpeed,
final double meanReversionLevel,
final double volatility,
final double timeWidth)
{
try
{
return new R1CIRStochasticEvolver (
meanReversionSpeed,
meanReversionLevel,
volatility,
new org.drip.dynamics.ito.R1WienerDriver (
timeWidth
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* R1CIRStochasticEvolver Constructor
*
* @param meanReversionSpeed The Mean Reversion Speed
* @param meanReversionLevel The Mean Reversion Level
* @param volatilityCoefficient The Volatility Coefficient
* @param r1StochasticDriver The Stochastic Driver
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public R1CIRStochasticEvolver (
final double meanReversionSpeed,
final double meanReversionLevel,
final double volatilityCoefficient,
final org.drip.dynamics.ito.R1StochasticDriver r1StochasticDriver)
throws java.lang.Exception
{
super (
org.drip.dynamics.meanreverting.CKLSParameters.CoxIngersollRoss (
meanReversionSpeed,
meanReversionLevel,
volatilityCoefficient
),
r1StochasticDriver
);
}
/**
* Indicate it the Evolution includes Zero, or is strictly Positive
*
* @return TRUE - Evoltuion is Strictly Positive
*/
public boolean evolutionStrictlyPositive()
{
org.drip.dynamics.meanreverting.CKLSParameters cklsParameters = cklsParameters();
double volatilityCoefficient = cklsParameters.volatilityCoefficient();
return 2. * cklsParameters.meanReversionSpeed() * cklsParameters.meanReversionLevel() >=
volatilityCoefficient * volatilityCoefficient;
}
/**
* Compute the Expected Value of x at a time t from a Starting Value x0
*
* @param x0 Starting Variate
* @param t Time
*
* @return Expected Value of x
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double mean (
final double x0,
final double t)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
x0
) || !org.drip.numerical.common.NumberUtil.IsValid (
t
) || 0. > t
)
{
throw new java.lang.Exception (
"R1CIRStochasticEvolver::mean => Invalid Inputs"
);
}
double timeDecayFactor = java.lang.Math.exp (
-1. * cklsParameters().meanReversionSpeed() * t
);
return x0 * timeDecayFactor + cklsParameters().meanReversionLevel() * (1. - timeDecayFactor);
}
/**
* Compute the Time Variance of x across at a Time Value t
*
* @param x0 Starting Variate
* @param t Time t
*
* @return Time Variance of x
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double timeVariance (
final double x0,
final double t)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
t
) || 0. > t
)
{
throw new java.lang.Exception (
"R1VasicekStochasticEvolver::timeCovariance => Invalid Inputs"
);
}
double volatilityCoefficient = cklsParameters().volatilityCoefficient();
double meanReversionSpeed = cklsParameters().meanReversionSpeed();
double timeDecayFactor = java.lang.Math.exp (
-1. * meanReversionSpeed * t
);
double oneMinusTimeDecayFactor = 1. - timeDecayFactor;
return volatilityCoefficient * volatilityCoefficient / meanReversionSpeed * oneMinusTimeDecayFactor *
(
x0 * timeDecayFactor + 0.5 * cklsParameters().meanReversionLevel() * oneMinusTimeDecayFactor
);
}
@Override public org.drip.measure.statistics.PopulationCentralMeasures
temporalPopulationCentralMeasures (
final double x0,
final double t)
{
try
{
return new org.drip.measure.statistics.PopulationCentralMeasures (
mean (
x0,
t
),
timeVariance (
x0,
t
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
@Override public org.drip.measure.statistics.PopulationCentralMeasures
steadyStatePopulationCentralMeasures (
final double x0)
{
double volatility = cklsParameters().volatilityCoefficient();
try
{
return new org.drip.measure.statistics.PopulationCentralMeasures (
cklsParameters().meanReversionLevel(),
0.5 * volatility * volatility / cklsParameters().meanReversionSpeed()
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
@Override public org.drip.measure.chisquare.R1NonCentral futureValueDistribution (
final double r0,
final double t)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
r0
) || !org.drip.numerical.common.NumberUtil.IsValid (
t
) || 0. > t
)
{
return null;
}
int digammaTermCount = 1000;
int besselFirstTermCount = 20;
org.drip.dynamics.meanreverting.CKLSParameters cklsParameters = cklsParameters();
double ePowerMinusAT = java.lang.Math.exp (
-1. * cklsParameters.meanReversionSpeed() * t
);
org.drip.function.definition.R1ToR1 gammaEstimator =
new org.drip.specialfunction.gamma.EulerIntegralSecondKind (
null
);
try
{
return new org.drip.measure.chisquare.R1NonCentral (
new org.drip.measure.chisquare.R1NonCentralParameters (
cklsParameters.meanReversionLevel() * (1. - ePowerMinusAT),
r0 * ePowerMinusAT
),
gammaEstimator,
org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (
digammaTermCount
),
new org.drip.function.definition.R2ToR1()
{
@Override public double evaluate (
final double s,
final double t)
throws Exception
{
return new org.drip.specialfunction.incompletegamma.LowerEulerIntegral (
null,
t
).evaluate (
s
);
}
},
org.drip.specialfunction.bessel.ModifiedFirstFrobeniusSeriesEstimator.Standard (
gammaEstimator,
besselFirstTermCount
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
@Override public org.drip.dynamics.kolmogorov.R1FokkerPlanckCIR fokkerPlanckGenerator()
{
try
{
return new org.drip.dynamics.kolmogorov.R1FokkerPlanckCIR (
cklsParameters()
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}