BurgardKjaerOperator.java
package org.drip.xva.pde;
/*
* -*- 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>BurgardKjaerOperator</i> sets up the Parabolic Differential Equation PDE based on the Ito Evolution
* Differential for the Reference Underlier Asset, as laid out in Burgard and Kjaer (2014). The References
* are:
*
* <br><br>
* <ul>
* <li>
* Burgard, C., and M. Kjaer (2014): PDE Representations of Derivatives with Bilateral Counter-party
* Risk and Funding Costs <i>Journal of Credit Risk</i> <b>7 (3)</b> 1-19
* </li>
* <li>
* Cesari, G., J. Aquilina, N. Charpillon, X. Filipovic, G. Lee, and L. Manda (2009): <i>Modeling,
* Pricing, and Hedging Counter-party Credit Exposure - A Technical Guide</i> <b>Springer
* Finance</b> New York
* </li>
* <li>
* Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk <i>Risk</i> <b>20 (2)</b>
* 86-90
* </li>
* <li>
* Li, B., and Y. Tang (2007): <i>Quantitative Analysis, Derivatives Modeling, and Trading
* Strategies in the Presence of Counter-party Credit Risk for the Fixed Income Market</i>
* <b>World Scientific Publishing</b> Singapore
* </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/XVAAnalyticsLibrary.md">XVA Analytics Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/xva/README.md">Valuation Adjustments that account for Collateral, CC Credit/Debt and Funding Overhead</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/xva/pde/README.md">Burgard Kjaer PDE Evolution Scheme</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class BurgardKjaerOperator
{
private org.drip.xva.definition.PDEEvolutionControl _pdeEvolutionControl = null;
private org.drip.exposure.evolver.PrimarySecurityDynamicsContainer _tradeablesContainer = null;
/**
* BurgardKjaerOperator Constructor
*
* @param tradeablesContainer The Universe of Tradeable Assets
* @param pdeEvolutionControl The XVA Control Settings
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public BurgardKjaerOperator (
final org.drip.exposure.evolver.PrimarySecurityDynamicsContainer tradeablesContainer,
final org.drip.xva.definition.PDEEvolutionControl pdeEvolutionControl)
throws java.lang.Exception
{
if (null == (_tradeablesContainer = tradeablesContainer) ||
null == (_pdeEvolutionControl = pdeEvolutionControl))
{
throw new java.lang.Exception ("BurgardKjaerOperator Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Universe of Trade-able Assets
*
* @return The Universe of Trade-able Assets
*/
public org.drip.exposure.evolver.PrimarySecurityDynamicsContainer tradeablesContainer()
{
return _tradeablesContainer;
}
/**
* Retrieve the XVA Control Settings
*
* @return The XVA Control Settings
*/
public org.drip.xva.definition.PDEEvolutionControl pdeEvolutionControl()
{
return _pdeEvolutionControl;
}
/**
* Generate the Derivative Value Time Increment using the Burgard Kjaer Scheme
*
* @param marketEdge The Market Edge
* @param initialTrajectoryVertex The Evolution Trajectory Vertex
* @param collateral The Off-setting Collateral
*
* @return The Time Increment using the Burgard Kjaer Scheme
*/
public org.drip.xva.pde.BurgardKjaerEdgeRun edgeRun (
final org.drip.exposure.universe.MarketEdge marketEdge,
final org.drip.xva.derivative.EvolutionTrajectoryVertex initialTrajectoryVertex,
final double collateral)
{
if (null == marketEdge ||
null == initialTrajectoryVertex ||
!org.drip.numerical.common.NumberUtil.IsValid (collateral))
{
return null;
}
org.drip.exposure.universe.MarketVertex finalMarketVertex = marketEdge.finish();
org.drip.exposure.universe.MarketVertexEntity finalDealerMarketVertex = finalMarketVertex.dealer();
org.drip.exposure.universe.MarketVertexEntity finalClientMarketVertex = finalMarketVertex.client();
org.drip.xva.derivative.PositionGreekVertex initialPositionGreekVertex =
initialTrajectoryVertex.positionGreekVertex();
double initialDerivativeXVAValue = initialPositionGreekVertex.derivativeXVAValue();
double gainOnDealerDefault = initialTrajectoryVertex.gainOnDealerDefault();
double dealerSeniorDefaultIntensity = finalDealerMarketVertex.hazardRate();
double clientDefaultIntensity = finalClientMarketVertex.hazardRate();
double dealerGainOnClientDefault = initialTrajectoryVertex.gainOnClientDefault();
double gainOnClientDefault = clientDefaultIntensity * dealerGainOnClientDefault;
try
{
double initialPortfolioValue = finalMarketVertex.latentStateValue
(_tradeablesContainer.assetList().get (0).label());
double portfolioValueBump = _pdeEvolutionControl.sensitivityShiftFactor() *
initialPortfolioValue;
double[] bumpedThetaArray = new org.drip.xva.pde.ParabolicDifferentialOperator
(_tradeablesContainer.assetList().get (0)).thetaUpDown (
initialTrajectoryVertex,
initialPortfolioValue,
portfolioValueBump
);
if (null == bumpedThetaArray || 3 != bumpedThetaArray.length)
{
return null;
}
return new org.drip.xva.pde.BurgardKjaerEdgeRun (
portfolioValueBump,
-1. * bumpedThetaArray[0],
-1. * bumpedThetaArray[1],
-1. * bumpedThetaArray[2],
finalMarketVertex.csaReplicator() * collateral,
(dealerSeniorDefaultIntensity + clientDefaultIntensity) * initialDerivativeXVAValue,
-1. * dealerSeniorDefaultIntensity * gainOnDealerDefault,
-1. * gainOnClientDefault,
0.
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Time Increment Run Attribution using the Burgard Kjaer Scheme
*
* @param marketEdge The Market Edge
* @param initialTrajectoryVertex The Starting Evolution Trajectory Vertex
* @param collateral The Off-setting Collateral
*
* @return The Time Increment Run Attribution using the Burgard Kjaer Scheme
*/
public org.drip.xva.pde.BurgardKjaerEdgeAttribution edgeRunAttribution (
final org.drip.exposure.universe.MarketEdge marketEdge,
final org.drip.xva.derivative.EvolutionTrajectoryVertex initialTrajectoryVertex,
final double collateral)
{
if (null == marketEdge ||
null == initialTrajectoryVertex)
{
return null;
}
org.drip.exposure.universe.MarketVertex finalMarketVertex = marketEdge.finish();
double derivativeXVAValue = initialTrajectoryVertex.positionGreekVertex().derivativeXVAValue();
org.drip.exposure.universe.MarketVertexEntity finalDealerMarketVertex = finalMarketVertex.dealer();
org.drip.exposure.universe.MarketVertexEntity finalClientMarketVertex = finalMarketVertex.client();
double clientRecoveryRate = finalClientMarketVertex.seniorRecoveryRate();
double dealerDefaultIntensity = finalDealerMarketVertex.hazardRate();
double clientDefaultIntensity = finalClientMarketVertex.hazardRate();
double closeOutMTM = org.drip.xva.definition.PDEEvolutionControl.CLOSEOUT_GREGORY_LI_TANG ==
_pdeEvolutionControl.closeOutScheme() ? derivativeXVAValue : derivativeXVAValue;
double dealerExposure = closeOutMTM > 0. ? closeOutMTM : finalDealerMarketVertex.seniorRecoveryRate()
* closeOutMTM;
double derivativeXVAClientDefaultGrowth = -1. * clientDefaultIntensity *
(closeOutMTM < 0. ? closeOutMTM : clientRecoveryRate * closeOutMTM);
double dealerSeniorFundingSpread = finalDealerMarketVertex.seniorFundingSpread() /
marketEdge.vertexIncrement();
try
{
double initialPortfolioValue = finalMarketVertex.latentStateValue
(_tradeablesContainer.assetList().get (0).label());
double portfolioValueBump = _pdeEvolutionControl.sensitivityShiftFactor() *
initialPortfolioValue;
double[] bumpedThetaArray = new org.drip.xva.pde.ParabolicDifferentialOperator
(_tradeablesContainer.assetList().get (0)).thetaUpDown (
initialTrajectoryVertex,
initialPortfolioValue,
portfolioValueBump
);
if (null == bumpedThetaArray || 3 != bumpedThetaArray.length)
{
return null;
}
return new org.drip.xva.pde.BurgardKjaerEdgeAttribution (
portfolioValueBump,
-1. * bumpedThetaArray[0],
-1. * bumpedThetaArray[1],
-1. * bumpedThetaArray[2],
finalMarketVertex.csaReplicator() * collateral,
(dealerDefaultIntensity + clientDefaultIntensity) * derivativeXVAValue,
dealerSeniorFundingSpread * dealerExposure,
-1. * dealerDefaultIntensity * dealerExposure,
derivativeXVAClientDefaultGrowth
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}