FundingBasisEvolver.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>FundingBasisEvolver</i> implements a Two Factor Stochastic Funding Model Evolver with a Log Normal
* Forward Process and a Mean Reverting Diffusion Process for the Funding Spread. 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 FundingBasisEvolver
{
private double _correlation = java.lang.Double.NaN;
private org.drip.measure.dynamics.DiffusionEvaluatorLogarithmic _underlyingEvolver = null;
private org.drip.measure.dynamics.DiffusionEvaluatorMeanReversion _fundingSpreadEvolver = null;
/**
* FundingBasisEvolver Constructor
*
* @param underlyingEvolver The Underlying Diffusion Evolver
* @param fundingSpreadEvolver The Funding Spread Diffusion Evolver
* @param correlation Correlation between the Underlying and the Funding Spread Processes
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public FundingBasisEvolver (
final org.drip.measure.dynamics.DiffusionEvaluatorLogarithmic underlyingEvolver,
final org.drip.measure.dynamics.DiffusionEvaluatorMeanReversion fundingSpreadEvolver,
final double correlation)
throws java.lang.Exception
{
if (null == (_underlyingEvolver = underlyingEvolver) ||
null == (_fundingSpreadEvolver = fundingSpreadEvolver) ||
!org.drip.numerical.common.NumberUtil.IsValid (_correlation = correlation) ||
1. < _correlation || -1. > _correlation)
{
throw new java.lang.Exception ("FundingBasisEvolver Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Underlying Diffusion Evolver
*
* @return The Underlying Diffusion Evolver
*/
public org.drip.measure.dynamics.DiffusionEvaluatorLogarithmic underlyingEvolver()
{
return _underlyingEvolver;
}
/**
* Retrieve the Funding Spread Diffusion Evolver
*
* @return The Funding Spread Diffusion Evolver
*/
public org.drip.measure.dynamics.DiffusionEvaluatorMeanReversion fundingSpreadEvolver()
{
return _fundingSpreadEvolver;
}
/**
* Retrieve the Correlation between the Underlying and the Funding Spread Processes
*
* @return The Correlation between the Underlying and the Funding Spread Processes
*/
public double underlyingFundingSpreadCorrelation()
{
return _correlation;
}
/**
* Generate the CSA Forward Diffusion Process
*
* @return The CSA Forward Diffusion Process
*/
public org.drip.measure.process.DiffusionEvolver csaForwardProcess()
{
try
{
org.drip.measure.dynamics.LocalEvaluator driftEvolver = new
org.drip.measure.dynamics.LocalEvaluator()
{
@Override public double value (
final org.drip.measure.realization.JumpDiffusionVertex vertex)
throws java.lang.Exception
{
return 0.;
}
};
org.drip.measure.dynamics.LocalEvaluator volatilityEvolver = new
org.drip.measure.dynamics.LocalEvaluator()
{
@Override public double value (
final org.drip.measure.realization.JumpDiffusionVertex vertex)
throws java.lang.Exception
{
if (null == vertex)
throw new java.lang.Exception
("FundingBasisEvolver::CSAForwardVolatility::Evaluator::value => Invalid Inputs");
return vertex.value() * _underlyingEvolver.volatilityValue();
}
};
return new org.drip.measure.process.DiffusionEvolver (
new org.drip.measure.dynamics.DiffusionEvaluator (
driftEvolver,
volatilityEvolver
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Funding Numeraire Diffusion Process
*
* @param tenor The Tenor of the Underlying Forward
*
* @return The Funding Numeraire Diffusion Process
*/
public org.drip.measure.process.DiffusionEvolver fundingNumeraireProcess (
final java.lang.String tenor)
{
try {
double meanReversionSpeed = _fundingSpreadEvolver.meanReversionRate();
double b = org.drip.analytics.support.Helper.TenorToYearFraction (tenor);
if (0. != meanReversionSpeed)
{
b = (1. - java.lang.Math.exp (-1. * meanReversionSpeed * b)) / meanReversionSpeed;
}
final double piterbarg2010BFactor = b;
org.drip.measure.dynamics.LocalEvaluator driftEvaluator = new
org.drip.measure.dynamics.LocalEvaluator()
{
@Override public double value (
final org.drip.measure.realization.JumpDiffusionVertex jumpDiffusionVertex)
throws java.lang.Exception
{
return 0.;
}
};
org.drip.measure.dynamics.LocalEvaluator volatilityEvaluator = new
org.drip.measure.dynamics.LocalEvaluator()
{
@Override public double value (
final org.drip.measure.realization.JumpDiffusionVertex jumpDiffusionVertex)
throws java.lang.Exception
{
if (null == jumpDiffusionVertex)
{
throw new java.lang.Exception
("FundingBasisEvolver::CSAFundingNumeraireVolatility::Evaluator::value => Invalid Inputs");
}
return -1. * jumpDiffusionVertex.value() * piterbarg2010BFactor *
_fundingSpreadEvolver.volatilityValue();
}
};
return new org.drip.measure.process.DiffusionEvolver (
new org.drip.measure.dynamics.DiffusionEvaluator (
driftEvaluator,
volatilityEvaluator
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Funding Spread Numeraire Diffusion Process
*
* @param tenor The Tenor of the Underlying Forward
*
* @return The Funding Spread Numeraire Diffusion Process
*/
public org.drip.measure.process.DiffusionEvolver fundingSpreadNumeraireProcess (
final java.lang.String tenor)
{
try
{
double meanReversionSpeed = _fundingSpreadEvolver.meanReversionRate();
double b = org.drip.analytics.support.Helper.TenorToYearFraction (tenor);
if (0. != meanReversionSpeed)
{
b = (1. - java.lang.Math.exp (-1. * meanReversionSpeed * b)) / meanReversionSpeed;
}
final double piterbarg2010BFactor = b;
org.drip.measure.dynamics.LocalEvaluator driftEvaluator = new
org.drip.measure.dynamics.LocalEvaluator()
{
@Override public double value (
final org.drip.measure.realization.JumpDiffusionVertex jumpDiffusionVertex)
throws java.lang.Exception
{
return 0.;
}
};
org.drip.measure.dynamics.LocalEvaluator volatilityEvaluator = new
org.drip.measure.dynamics.LocalEvaluator()
{
@Override public double value (
final org.drip.measure.realization.JumpDiffusionVertex jumpDiffusionVertex)
throws java.lang.Exception
{
if (null == jumpDiffusionVertex)
{
throw new java.lang.Exception
("FundingBasisEvolver::CSAFundingSpreadNumeraireVolatility::Evaluator::value => Invalid Inputs");
}
return -1. * jumpDiffusionVertex.value() * piterbarg2010BFactor *
_fundingSpreadEvolver.volatilityValue();
}
};
return new org.drip.measure.process.DiffusionEvolver (
new org.drip.measure.dynamics.DiffusionEvaluator (
driftEvaluator,
volatilityEvaluator
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Compute the CSA vs. No CSA Forward Ratio
*
* @param tenor The Tenor of the Underlying Forward
*
* @return The CSA vs. No CSA Forward Ratio
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double CSANoCSARatio (
final java.lang.String tenor)
throws java.lang.Exception
{
double underlyingVolatility = _underlyingEvolver.volatilityValue();
double meanReversionSpeed = _fundingSpreadEvolver.meanReversionRate();
double fundingSpreadVolatility = _fundingSpreadEvolver.volatilityValue();
double maturity = org.drip.analytics.support.Helper.TenorToYearFraction (tenor);
if (0. == meanReversionSpeed)
{
return java.lang.Math.exp (-0.5 * _correlation * underlyingVolatility *
fundingSpreadVolatility * maturity * maturity);
}
double b = (1. - java.lang.Math.exp (-1. * meanReversionSpeed * maturity)) /
meanReversionSpeed;
return java.lang.Math.exp (-1. * _correlation * underlyingVolatility *
fundingSpreadVolatility * (maturity - b) / meanReversionSpeed);
}
}