ExponentialAffineZeroCoefficients.java
package org.drip.dynamics.physical;
/*
* -*- 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>ExponentialAffineZeroCoefficients</i> contains the Exponential Affine Coefficients for a Zero-coupon
* Bond priced using the CIR Process. 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/physical/README.md">Implementation of Physical Process Dynamics</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ExponentialAffineZeroCoefficients
{
private double _A = java.lang.Double.NaN;
private double _B = java.lang.Double.NaN;
/**
* Construct an Instance of ExponentialAffineZeroCoefficients using the CIR Stochastic Evolver
*
* @param r1CIRStochasticEvolver The CIR Stochastic Evolver
* @param ttm The Time to Maturity
*
* @return The ExponentialAffineZeroCoefficients Instance
*/
public static final ExponentialAffineZeroCoefficients FromCIR (
final org.drip.dynamics.meanreverting.R1CIRStochasticEvolver r1CIRStochasticEvolver,
final double ttm)
{
if (null == r1CIRStochasticEvolver ||
!org.drip.numerical.common.NumberUtil.IsValid (
ttm
) || 0. > ttm
)
{
return null;
}
org.drip.dynamics.meanreverting.CKLSParameters cklsParameters =
r1CIRStochasticEvolver.cklsParameters();
double meanReversionSpeed = cklsParameters.meanReversionSpeed();
double volatilityCoefficient = cklsParameters.volatilityCoefficient();
double sigmaSquared = volatilityCoefficient * volatilityCoefficient;
double h = java.lang.Math.sqrt (
meanReversionSpeed * meanReversionSpeed + 2. * sigmaSquared
);
double hT = h * ttm;
double twoH = 2 * h;
double aPlusH = meanReversionSpeed + h;
double exp_hT_MinusOne = java.lang.Math.exp (
hT
) - 1.;
double inverseOfTwoHPlus_APlusHTimes__exp_hT_MinusOne__ = 1. / (
twoH + aPlusH * (
java.lang.Math.exp (
hT
) - 1.
)
);
try
{
return new ExponentialAffineZeroCoefficients (
java.lang.Math.pow (
twoH * java.lang.Math.exp (
0.5 * aPlusH * ttm
) * inverseOfTwoHPlus_APlusHTimes__exp_hT_MinusOne__,
2. * meanReversionSpeed * cklsParameters.meanReversionLevel() / sigmaSquared
),
2. * exp_hT_MinusOne * inverseOfTwoHPlus_APlusHTimes__exp_hT_MinusOne__
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* ExponentialAffineZeroCoefficients Constructor
*
* @param a Exponential Affine "A"
* @param b Exponential Affine "B"
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public ExponentialAffineZeroCoefficients (
final double a,
final double b)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
_A = a
) || !org.drip.numerical.common.NumberUtil.IsValid (
_B = b
)
)
{
throw new java.lang.Exception (
"ExponentialAffineZeroCoefficients Constructor => Invalid Inputs"
);
}
}
/**
* Retrieve Exponential Affine "A"
*
* @return The Exponential Affine "A"
*/
public double a()
{
return _A;
}
/**
* Retrieve Exponential Affine "B"
*
* @return The Exponential Affine "B"
*/
public double b()
{
return _B;
}
/**
* Compute the Price given the Initial Rate
*
* @param r0 The Initial Rate
*
* @return Price given the Initial Rate
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double price (
final double r0)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
r0
))
{
throw new java.lang.Exception (
"ExponentialAffineZeroCoefficients::price => Invalid Inputs"
);
}
return _A * java.lang.Math.exp (
-1. * _B * r0
);
}
}