CIRFutureValueDistribution.java
package org.drip.sample.ckls;
import org.drip.dynamics.meanreverting.R1CIRStochasticEvolver;
import org.drip.measure.chisquare.R1NonCentral;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
/*
* -*- 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 risk, transaction costs, exposure, margin
* calculations, valuation adjustment, and portfolio construction within and across fixed income,
* credit, commodity, equity, FX, and structured products.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
*
* DROP Analytics Core implements libraries for the following:
* - Fixed Income Analytics
* - Asset Backed Analytics
* - XVA Analytics
* - Exposure and Margin Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Transaction Cost Analytics
*
* DROP Numerical Core implements libraries for the following:
* - Statistical Learning Library
* - Numerical Optimizer Library
* - Machine Learning Library
* - Spline Builder Library
*
* 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>CIRFutureValueDistribution</i> demonstrates the Computation of the Future Value Distribution from an
* Evolving R<sup>1</sup> Cox-Ingersoll-Ross 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/sample/README.md">DROP API Construction and Usage</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/ckls/README.md">Analysis of CKLS Process Variants</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class CIRFutureValueDistribution
{
private static final void NonCentralChiSquareParameters (
final double r0,
final double meanReversionSpeed,
final double meanReversionLevel,
final double[] tArray)
throws Exception
{
R1CIRStochasticEvolver r1CIRStochasticEvolver = R1CIRStochasticEvolver.Wiener (
meanReversionSpeed,
meanReversionLevel,
0.05,
0.01
);
java.lang.String dump = "\t| [" +
FormatUtil.FormatDouble (meanReversionSpeed, 1, 1, 1.) + "," +
FormatUtil.FormatDouble (meanReversionLevel, 1, 1, 1.) + "] =>";
for (double t : tArray)
{
R1NonCentral r1NonCentral = r1CIRStochasticEvolver.futureValueDistribution (
r0,
t
);
dump = dump + " {" + FormatUtil.FormatDouble (
r1NonCentral.parameters().degreesOfFreedom(), 1, 4, 1.
) + " |" + FormatUtil.FormatDouble (
r1NonCentral.parameters().nonCentralityParameter(), 1, 4, 1.
) + "}";
}
System.out.println (dump);
}
private static final void NonCentralChiSquareStatistics (
final double r0,
final double meanReversionSpeed,
final double meanReversionLevel,
final double[] tArray)
throws Exception
{
R1CIRStochasticEvolver r1CIRStochasticEvolver = R1CIRStochasticEvolver.Wiener (
meanReversionSpeed,
meanReversionLevel,
0.05,
0.01
);
java.lang.String dump = "\t| [" +
FormatUtil.FormatDouble (meanReversionSpeed, 1, 1, 1.) + "," +
FormatUtil.FormatDouble (meanReversionLevel, 1, 1, 1.) + "] =>";
for (double t : tArray)
{
R1NonCentral r1NonCentral = r1CIRStochasticEvolver.futureValueDistribution (
r0,
t
);
dump = dump + " {" + FormatUtil.FormatDouble (
r1NonCentral.mean(), 1, 4, 1.
) + " |" + FormatUtil.FormatDouble (
r1NonCentral.variance(), 1, 4, 1.
) + "}";
}
System.out.println (dump);
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv (
""
);
double r0 = 3.0;
double[] tArray =
{
1.0,
2.0,
3.0,
4.0,
5.0,
6.0,
7.0,
};
double[] meanReversionLevelArray =
{
2.0,
3.0,
4.0,
};
double[] meanReversionSpeedArray =
{
0.5,
1.0,
1.5,
2.0,
2.5,
};
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| CIR FUTURE VALUE DISTRIBUTION ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Mean Reversion Speed ||");
System.out.println ("\t| - Mean Reversion Level ||");
System.out.println ("\t| - Volatility ||");
System.out.println ("\t| - Chi-Square Degrees of Freedom and Non-Centrality Parameter over t ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");
for (double meanReversionSpeed : meanReversionSpeedArray)
{
for (double meanReversionLevel : meanReversionLevelArray)
{
NonCentralChiSquareParameters (
r0,
meanReversionSpeed,
meanReversionLevel,
tArray
);
}
}
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println();
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| CIR FUTURE VALUE DISTRIBUTION ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Mean Reversion Speed ||");
System.out.println ("\t| - Mean Reversion Level ||");
System.out.println ("\t| - Volatility ||");
System.out.println ("\t| - Chi-Square Mean and Variance over t ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");
for (double meanReversionSpeed : meanReversionSpeedArray)
{
for (double meanReversionLevel : meanReversionLevelArray)
{
NonCentralChiSquareStatistics (
r0,
meanReversionSpeed,
meanReversionLevel,
tArray
);
}
}
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println();
EnvManager.TerminateEnv();
}
}