NumeraireInducedMeasureShift.java
package org.drip.exposure.csadynamics;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 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>NumeraireInducedMeasureShift</i> computes the Shift of the Forward Terminal Distribution between the
* Non-CSA and the CSA Cases. The References are:
*
* <br><br>
* <ul>
* <li>
* Antonov, A., and M. Arneguy (2009): Analytical Formulas for Pricing CMS Products in the LIBOR
* Market Model with Stochastic Volatility
* https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=1352606 <b>eSSRN</b>
* </li>
* <li>
* Burgard, C., and M. Kjaer (2009): Modeling and successful Management of Credit Counter-party
* Risk of Derivative Portfolios <i>ICBI Conference</i> <b>Rome</b>
* </li>
* <li>
* Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk <i>Risk</i> <b>20 (2)</b>
* 86-90
* </li>
* <li>
* Johannes, M., and S. Sundaresan (2007): Pricing Collateralized Swaps <i>Journal of
* Finance</i> <b>62</b> 383-410
* </li>
* <li>
* Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives
* Pricing <i>Risk</i> <b>21 (2)</b> 97-102
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ExposureAnalyticsLibrary.md">Exposure Analytics</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/exposure/README.md">Exposure Group Level Collateralized/Uncollateralized Exposure</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/exposure/csadynamics/README.md">CSA Numeraire Basis/Measure Dynamics</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class NumeraireInducedMeasureShift
{
private double _csaForward = java.lang.Double.NaN;
private double _noCSAForward = java.lang.Double.NaN;
private double _terminalVariance = java.lang.Double.NaN;
/**
* NumeraireInducedMeasureShift Constructor
*
* @param csaForward The CSA Implied Forward Value
* @param noCSAForward The No CSA Implied Forward Value
* @param terminalVariance The Terminal Variance of the Underlying
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public NumeraireInducedMeasureShift (
final double csaForward,
final double noCSAForward,
final double terminalVariance)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (_csaForward = csaForward) ||
!org.drip.numerical.common.NumberUtil.IsValid (_noCSAForward = noCSAForward) ||
!org.drip.numerical.common.NumberUtil.IsValid (_terminalVariance = terminalVariance))
{
throw new java.lang.Exception ("NumeraireInducedMeasureShift Constructor => Invalid Inputs");
}
}
/**
* Return the Value of the Forward Contract under CSA
*
* @return The Value of the Forward Contract under CSA
*/
public double csaForward()
{
return _csaForward;
}
/**
* Return the Value of the Forward Contract under No CSA Criterion
*
* @return The Value of the Forward Contract under No CSA Criterion
*/
public double noCSAForward()
{
return _noCSAForward;
}
/**
* Return the Terminal Variance of the Underlying
*
* @return The Terminal Variance of the Underlying
*/
public double terminalVariance()
{
return _terminalVariance;
}
/**
* Return the Linear Strike Coefficient of the Relative Measure Differential
*
* @return The Linear Strike Coefficient of the Relative Measure Differential
*/
public double alpha1()
{
return (_noCSAForward - _csaForward) / _terminalVariance;
}
/**
* Return the Constant Strike Coefficient of the Relative Measure Differential
*
* @return The Constant Strike Coefficient of the Relative Measure Differential
*/
public double alpha0()
{
return 1. - alpha1() * _csaForward;
}
/**
* Compute the No CSA/CSA Density Re-scaling using the Antonov and Arneguy (2009) Linear Proxy Approach
*
* @param k The Strike at which the Density Re-scaling is Sought
*
* @return The No CSA/CSA Density Re-scaling using the Antonov and Arneguy (2009) Linear Proxy Approach
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double densityRescale (
final double k)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (k))
{
throw new java.lang.Exception ("NumeraireInducedMeasureShift::densityRescale => Invalid Inputs");
}
double dblAlpha1 = (_noCSAForward - _csaForward) / _terminalVariance;
return 1. - dblAlpha1 * _csaForward + dblAlpha1 * k;
}
}