R1VasicekStochasticEvolver.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>R1VasicekStochasticEvolver</i> implements the R<sup>1</sup> Vasicek 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 R1VasicekStochasticEvolver
extends org.drip.dynamics.meanreverting.R1CKLSStochasticEvolver
{
/**
* Construct a Weiner Instance of R1VasicekStochasticEvolver 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 R1VasicekStochasticEvolver Process
*/
public static R1VasicekStochasticEvolver Wiener (
final double meanReversionSpeed,
final double meanReversionLevel,
final double volatility,
final double timeWidth)
{
try
{
return new R1VasicekStochasticEvolver (
meanReversionSpeed,
meanReversionLevel,
volatility,
new org.drip.dynamics.ito.R1WienerDriver (
timeWidth
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* R1VasicekStochasticEvolver Constructor
*
* @param meanReversionSpeed The Mean Reversion Speed
* @param meanReversionLevel The Mean Reversion Level
* @param volatility The Volatility
* @param r1StochasticDriver The Stochastic Driver
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public R1VasicekStochasticEvolver (
final double meanReversionSpeed,
final double meanReversionLevel,
final double volatility,
final org.drip.dynamics.ito.R1StochasticDriver r1StochasticDriver)
throws java.lang.Exception
{
super (
org.drip.dynamics.meanreverting.CKLSParameters.Vasicek (
meanReversionSpeed,
meanReversionLevel,
volatility
),
r1StochasticDriver
);
}
/**
* 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 (
"R1VasicekStochasticEvolver::mean => Invalid Inputs"
);
}
double timeDecayFactor = java.lang.Math.exp (
-1. * cklsParameters().meanReversionSpeed() * t
);
return x0 * timeDecayFactor + cklsParameters().meanReversionLevel() * (1. - timeDecayFactor);
}
/**
* Compute the Time Co-variance of x across Time Values t and s
*
* @param x0 Starting Variate
* @param s Time s
* @param t Time t
*
* @return Time Co-variance of x
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double timeCovariance (
final double x0,
final double s,
final double t)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
s
) || 0. > s || !org.drip.numerical.common.NumberUtil.IsValid (
t
) || 0. > t
)
{
throw new java.lang.Exception (
"R1VasicekStochasticEvolver::timeCovariance => Invalid Inputs"
);
}
double volatility = cklsParameters().volatilityCoefficient();
double meanReversionSpeed = cklsParameters().meanReversionSpeed();
return 0.5 * volatility * volatility / meanReversionSpeed *
(
(
java.lang.Math.exp (
-1. * meanReversionSpeed * java.lang.Math.abs (
s - t
)
) - java.lang.Math.exp (
-1. * meanReversionSpeed * (s + t)
)
)
);
}
@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
),
timeCovariance (
x0,
t,
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;
}
/**
* Construct the Ait-Sahalia Maximum Likelihood Estimation Sampling Interval Discreteness Error
*
* @param intervalWidth Sampling Interval Width
*
* @return The Ait-Sahalia Maximum Likelihood Estimation Sampling Interval Discreteness Error
*/
public double[][] aitSahaliaMLEAsymptote (
final double intervalWidth)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
intervalWidth
) || 0. >= intervalWidth
)
{
return null;
}
double volatility = cklsParameters().volatilityCoefficient();
double meanReversionSpeed = cklsParameters().meanReversionSpeed();
double tTheta = intervalWidth * meanReversionSpeed;
double tSquaredThetaSquared = tTheta * tTheta;
double ePower_TTheta_ = java.lang.Math.exp (
tTheta
);
double ePower_TwoTTheta_ = ePower_TTheta_ * ePower_TTheta_;
double ePower_TwoTTheta_MinusOne = ePower_TwoTTheta_ - 1.;
double sigmaSquared = volatility * volatility;
double[][] aitSahaliaMLEAsymptote = new double[3][3];
double tSquared = intervalWidth * intervalWidth;
aitSahaliaMLEAsymptote[0][0] = ePower_TwoTTheta_MinusOne / tSquared;
aitSahaliaMLEAsymptote[0][1] = 0.;
aitSahaliaMLEAsymptote[0][2] = sigmaSquared * ePower_TwoTTheta_MinusOne *
(ePower_TwoTTheta_MinusOne - 2. * intervalWidth) / tSquared / meanReversionSpeed;
aitSahaliaMLEAsymptote[1][0] = 0.;
aitSahaliaMLEAsymptote[1][1] = 0.5 * sigmaSquared * (ePower_TTheta_ + 1.) / (ePower_TTheta_ - 1.) /
meanReversionSpeed;
aitSahaliaMLEAsymptote[1][2] = 0.;
aitSahaliaMLEAsymptote[2][0] = aitSahaliaMLEAsymptote[0][2];
aitSahaliaMLEAsymptote[2][1] = 0.;
aitSahaliaMLEAsymptote[2][2] = sigmaSquared * sigmaSquared * (
ePower_TwoTTheta_MinusOne * ePower_TwoTTheta_MinusOne +
2. * tSquaredThetaSquared * (ePower_TwoTTheta_ + 1.) +
4. * tTheta * ePower_TwoTTheta_MinusOne
) / (ePower_TwoTTheta_MinusOne * tSquaredThetaSquared);
return aitSahaliaMLEAsymptote;
}
}