DiffusionTensor.java
package org.drip.dynamics.ito;
/*
* -*- 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>DiffusionTensor</i> Diffusion Tensor generates Cross-Product from the Multivariate Volatility
* Functions. 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/ito/README.md">Ito Stochastic Process Dynamics Foundation</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class DiffusionTensor
{
private org.drip.dynamics.ito.RdToR1Volatility[][] _volatilityFunctionGrid = null;
/**
* DiffusionTensor Constructor
*
* @param volatilityFunctionGrid Square Volatility Grid
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public DiffusionTensor (
final org.drip.dynamics.ito.RdToR1Volatility[][] volatilityFunctionGrid)
throws java.lang.Exception
{
if (null == (_volatilityFunctionGrid = volatilityFunctionGrid))
{
throw new java.lang.Exception (
"DiffusionTensor Constructor => Invalid Inputs"
);
}
int factorCount = 0;
int dimension = _volatilityFunctionGrid.length;
if (0 == dimension)
{
throw new java.lang.Exception (
"DiffusionTensor Constructor => Invalid Inputs"
);
}
for (int dimensionIndex = 0;
dimensionIndex < dimension;
++dimensionIndex)
{
if (null == _volatilityFunctionGrid[dimensionIndex])
{
throw new java.lang.Exception (
"DiffusionTensor Constructor => Invalid Inputs"
);
}
if (0 == dimensionIndex)
{
if (0 == (factorCount = _volatilityFunctionGrid[dimensionIndex].length))
{
throw new java.lang.Exception (
"DiffusionTensor Constructor => Invalid Inputs"
);
}
}
if (null == _volatilityFunctionGrid[dimensionIndex] ||
factorCount != _volatilityFunctionGrid[dimensionIndex].length)
{
throw new java.lang.Exception (
"DiffusionTensor Constructor => Invalid Inputs"
);
}
}
}
/**
* Retrieve the Square Volatility Grid
*
* @return The Square Volatility Grid
*/
public org.drip.dynamics.ito.RdToR1Volatility[][] volatilityFunctionGrid()
{
return _volatilityFunctionGrid;
}
/**
* Retrieve the Dimension Count
*
* @return The Dimension Count
*/
public int dimension()
{
return _volatilityFunctionGrid.length;
}
/**
* Retrieve the Factor Count
*
* @return The Factor Count
*/
public int factorCount()
{
return _volatilityFunctionGrid[0].length;
}
/**
* Estimate the Diffusion Coefficient
*
* @param timeRdVertex R<sup>d</sup> Property Variate/Time Coordinate Vertex
* @param variateIndexI Variate Index I
* @param variateIndexJ Variate Index J
*
* @return The Diffusion Coefficient
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double diffusionCoefficient (
final org.drip.dynamics.ito.TimeRdVertex timeRdVertex,
final int variateIndexI,
final int variateIndexJ)
throws java.lang.Exception
{
if (null == timeRdVertex)
{
throw new java.lang.Exception (
"DiffusionTensor::diffusionCoefficient => Invalid Inputs"
);
}
double diffusionCoefficient = 0.;
int dimension = _volatilityFunctionGrid.length;
int factorCount = _volatilityFunctionGrid[0].length;
if (dimension >= variateIndexI || dimension >= variateIndexJ)
{
throw new java.lang.Exception (
"DiffusionTensor::diffusionCoefficient => Invalid Inputs"
);
}
for (int factorIndex = 0;
factorIndex < factorCount;
++factorIndex)
{
diffusionCoefficient = diffusionCoefficient +
_volatilityFunctionGrid[variateIndexI][factorIndex].volatility (
timeRdVertex
) * _volatilityFunctionGrid[variateIndexJ][factorIndex].volatility (
timeRdVertex
);
}
return 0.5 * diffusionCoefficient;
}
}