XVAReplicationPortfolio.java
package org.drip.sample.burgard2011;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import org.drip.analytics.date.*;
import org.drip.analytics.support.VertexDateBuilder;
import org.drip.exposure.evolver.*;
import org.drip.exposure.universe.*;
import org.drip.measure.crng.RandomNumberGenerator;
import org.drip.measure.discrete.CorrelatedPathVertexDimension;
import org.drip.measure.dynamics.*;
import org.drip.measure.process.*;
import org.drip.measure.realization.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.linearalgebra.Matrix;
import org.drip.service.env.EnvManager;
import org.drip.state.identifier.*;
import org.drip.xva.definition.*;
import org.drip.xva.derivative.*;
import 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>XVAReplicationPortfolio</i> demonstrates the Bank and Counter-Party Default Based Derivative Evolution
* of the Dynamic XVA Replication Porfolio. 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/sample/README.md">DROP API Construction and Usage</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/burgard2011/README.md">Burgard Kjaer (2011) PDE Evolver</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class XVAReplicationPortfolio {
private static final PrimarySecurity AssetValueReplicator (
final String currency)
throws Exception
{
double assetValueReplicatorDrift = 0.0025;
double assetValueReplicatorVolatility = 0.10;
double assetValueReplicatorRepo = 0.03;
double assetValueReplicatorDividend = 0.02;
EntityEquityLabel equityLabel = EntityEquityLabel.Standard (
"AAPL",
currency
);
return new PrimarySecurity (
"AAPL",
equityLabel,
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
assetValueReplicatorDrift - assetValueReplicatorDividend,
assetValueReplicatorVolatility
)
),
assetValueReplicatorRepo
);
}
private static final PrimarySecurity OvernightReplicator (
final String currency,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double overnightReplicatorDrift = 0.0025;
double overnightReplicatorVolatility = 0.001;
double overnightReplicatorRepo = 0.0;
LatentStateLabel overnightLabel = OvernightLabel.Create (currency);
latentStateLabelList.add (overnightLabel);
return new PrimarySecurity (
currency + "_OVERNIGHT",
overnightLabel,
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
overnightReplicatorDrift,
overnightReplicatorVolatility
)
),
overnightReplicatorRepo
);
}
private static final PrimarySecurity CSAReplicator (
final String currency,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double csaReplicatorDrift = 0.01;
double csaReplicatorVolatility = 0.002;
double csaReplicatorRepo = 0.005;
LatentStateLabel csaLabel = CSALabel.ISDA (currency);
latentStateLabelList.add (csaLabel);
return new PrimarySecurity (
currency + "_CSA",
csaLabel,
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
csaReplicatorDrift,
csaReplicatorVolatility
)
),
csaReplicatorRepo
);
}
private static final PrimarySecurity DealerSeniorFundingReplicator (
final String currency,
final String dealer,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double dealerSeniorFundingReplicatorDrift = 0.03;
double dealerSeniorFundingReplicatorVolatility = 0.002;
double dealerSeniorFundingReplicatorRepo = 0.028;
LatentStateLabel dealerSeniorFundingLabel = EntityFundingLabel.Senior (
dealer,
currency
);
latentStateLabelList.add (dealerSeniorFundingLabel);
return new PrimarySecurity (
dealer + "_" + currency + "_SENIOR_ZERO",
dealerSeniorFundingLabel,
new JumpDiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dealerSeniorFundingReplicatorDrift,
dealerSeniorFundingReplicatorVolatility
),
HazardJumpEvaluator.Standard (
0.3,
0.45
)
),
dealerSeniorFundingReplicatorRepo
);
}
private static final PrimarySecurity DealerSubordinateFundingReplicator (
final String currency,
final String dealer,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double dealerSubordinateFundingReplicatorDrift = 0.045;
double dealerSubordinateFundingReplicatorVolatility = 0.002;
double dealerSubordinateFundingReplicatorRepo = 0.028;
LatentStateLabel dealerSubordinateFundingLabel = EntityFundingLabel.Subordinate (
dealer,
currency
);
latentStateLabelList.add (dealerSubordinateFundingLabel);
return new PrimarySecurity (
dealer + "_" + currency + "_SUBORDINATE_ZERO",
dealerSubordinateFundingLabel,
new JumpDiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dealerSubordinateFundingReplicatorDrift,
dealerSubordinateFundingReplicatorVolatility
),
HazardJumpEvaluator.Standard (
0.3,
0.25
)
),
dealerSubordinateFundingReplicatorRepo
);
}
private static final PrimarySecurity ClientFundingReplicator (
final String currency,
final String client,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double clientFundingReplicatorDrift = 0.03;
double clientFundingReplicatorVolatility = 0.003;
double clientFundingReplicatorRepo = 0.028;
LatentStateLabel clientFundingLabel = EntityFundingLabel.Senior (
client,
currency
);
latentStateLabelList.add (clientFundingLabel);
return new PrimarySecurity (
client + "_" + currency + "_SENIOR_ZERO",
clientFundingLabel,
new JumpDiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
clientFundingReplicatorDrift,
clientFundingReplicatorVolatility
),
HazardJumpEvaluator.Standard (
0.5,
0.30
)
),
clientFundingReplicatorRepo
);
}
private static final PrimarySecurityDynamicsContainer PrimarySecurityEvolver (
final String currency,
final String dealer,
final String client,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
List<PrimarySecurity> assetList = new ArrayList<PrimarySecurity>();
assetList.add (AssetValueReplicator (currency));
return new PrimarySecurityDynamicsContainer (
assetList,
OvernightReplicator (
currency,
latentStateLabelList
),
CSAReplicator (
currency,
latentStateLabelList
),
DealerSeniorFundingReplicator (
currency,
dealer,
latentStateLabelList
),
DealerSubordinateFundingReplicator (
currency,
dealer,
latentStateLabelList
),
ClientFundingReplicator (
currency,
client,
latentStateLabelList
)
);
}
private static final TerminalLatentState DealerHazard (
final String currency,
final String dealer,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double dealerHazardDrift = 0.0002;
double dealerHazardVolatility = 0.02;
LatentStateLabel dealerHazardLabel = EntityHazardLabel.Standard (
dealer,
currency
);
latentStateLabelList.add (dealerHazardLabel);
return new TerminalLatentState (
dealerHazardLabel,
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dealerHazardDrift,
dealerHazardVolatility
)
)
);
}
private static final TerminalLatentState DealerRecovery (
final String currency,
final String dealer,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double dealerRecoveryDrift = 0.0002;
double dealerRecoveryVolatility = 0.02;
LatentStateLabel dealerRecoveryLabel = EntityRecoveryLabel.Senior (
dealer,
currency
);
latentStateLabelList.add (dealerRecoveryLabel);
return new TerminalLatentState (
dealerRecoveryLabel,
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dealerRecoveryDrift,
dealerRecoveryVolatility
)
)
);
}
private static final TerminalLatentState ClientHazard (
final String currency,
final String client,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double clientHazardDrift = 0.0002;
double clientHazardVolatility = 0.02;
LatentStateLabel clientHazardLabel = EntityHazardLabel.Standard (
client,
currency
);
latentStateLabelList.add (clientHazardLabel);
return new TerminalLatentState (
clientHazardLabel,
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
clientHazardDrift,
clientHazardVolatility
)
)
);
}
private static final TerminalLatentState ClientRecovery (
final String currency,
final String client,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double clientRecoveryDrift = 0.0002;
double clientRecoveryVolatility = 0.02;
LatentStateLabel clientRecoveryLabel = EntityRecoveryLabel.Senior (
client,
currency
);
latentStateLabelList.add (clientRecoveryLabel);
return new TerminalLatentState (
clientRecoveryLabel,
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
clientRecoveryDrift,
clientRecoveryVolatility
)
)
);
}
private static final EntityDynamicsContainer EntityEvolver (
final String currency,
final String dealer,
final String client,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
return new EntityDynamicsContainer (
DealerHazard (
currency,
dealer,
latentStateLabelList
),
DealerRecovery (
currency,
dealer,
latentStateLabelList
),
null,
ClientHazard (
currency,
client,
latentStateLabelList
),
ClientRecovery (
currency,
client,
latentStateLabelList
)
);
}
private static final LatentStateDynamicsContainer LatentStateEvolver (
final EntityEquityLabel equityLabel,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double assetValueReplicatorDrift = 0.0025;
double assetValueReplicatorVolatility = 0.10;
latentStateLabelList.add (equityLabel);
LatentStateDynamicsContainer latentStateDynamicsContainer = new LatentStateDynamicsContainer();
latentStateDynamicsContainer.addEntityEquity (
new TerminalLatentState (
equityLabel,
new DiffusionEvolver (
DiffusionEvaluatorLinear.Standard (
assetValueReplicatorDrift,
assetValueReplicatorVolatility
)
)
)
);
return latentStateDynamicsContainer;
}
private static final MarketVertexGenerator ConstructMarketVertexGenerator (
final JulianDate spotDate,
final int[] eventVertexArray,
final String currency,
final String dealer,
final String client,
final EntityEquityLabel equityLabel,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
return new MarketVertexGenerator (
spotDate.julian(),
eventVertexArray,
EntityEvolver (
currency,
dealer,
client,
latentStateLabelList
),
PrimarySecurityEvolver (
currency,
dealer,
client,
latentStateLabelList
),
LatentStateEvolver (
equityLabel,
latentStateLabelList
)
);
}
private static final MarketVertex[] MarketVertexArray (
final Map<Integer, MarketVertex> marketVertexMap)
throws Exception
{
int marketVertexCount = marketVertexMap.size();
int marketVertexIndex = 0;
MarketVertex[] marketVertexArray = new MarketVertex[marketVertexCount];
for (Map.Entry<Integer, MarketVertex> marketVertexMapEntry : marketVertexMap.entrySet())
{
marketVertexArray[marketVertexIndex++] = marketVertexMapEntry.getValue();
}
return marketVertexArray;
}
private static final EvolutionTrajectoryVertex RunStep (
final TrajectoryEvolutionScheme tes,
final BurgardKjaerOperator bko,
final EvolutionTrajectoryVertex etvStart,
final MarketVertex mvStart,
final MarketVertex mvFinish,
final LatentStateLabel equityLabel)
throws Exception
{
PositionGreekVertex agvStart = etvStart.positionGreekVertex();
ReplicationPortfolioVertex rpvStart = etvStart.replicationPortfolioVertex();
double dblDerivativeXVAValueStart = agvStart.derivativeXVAValue();
double dblTimeWidth = (mvFinish.anchorDate().julian() - mvStart.anchorDate().julian()) / 365.;
double dblTimeStart = etvStart.time();
double dblTime = dblTimeStart + dblTimeWidth;
double dblCollateralSchemeNumeraire = mvStart.csaReplicator();
PrimarySecurityDynamicsContainer tc = tes.tradeablesContainer();
BurgardKjaerEdgeRun bker = bko.edgeRun (
new MarketEdge (
mvStart,
mvFinish
),
etvStart,
0.
);
double dblTheta = bker.theta();
double dblAssetNumeraireBump = bker.positionValueBump();
double dblThetaAssetNumeraireUp = bker.thetaPositionValueUp();
double dblThetaAssetNumeraireDown = bker.thetaPositionValueDown();
double dblDerivativeXVAValueDeltaFinish = agvStart.derivativeXVAValueDelta() -
0.5 * (dblThetaAssetNumeraireUp - dblThetaAssetNumeraireDown) * dblTimeWidth / dblAssetNumeraireBump;
double dblDerivativeXVAValueGammaFinish = agvStart.derivativeXVAValueGamma() -
(dblThetaAssetNumeraireUp + dblThetaAssetNumeraireDown - 2. * dblTheta) * dblTimeWidth /
(dblAssetNumeraireBump * dblAssetNumeraireBump);
double dblDerivativeXVAValueFinish = dblDerivativeXVAValueStart + dblTheta * dblTimeWidth;
CloseOut cog = new CloseOutBilateral (
mvStart.dealer().seniorRecoveryRate(),
mvStart.client().seniorRecoveryRate()
);
double dblGainOnBankDefaultFinish = -1. * (dblDerivativeXVAValueFinish - cog.dealerDefault
(dblDerivativeXVAValueFinish));
double dblGainOnCounterPartyDefaultFinish = -1. * (dblDerivativeXVAValueFinish - cog.clientDefault
(dblDerivativeXVAValueFinish));
CashAccountEdge cae = tes.rebalanceCash (
etvStart,
new MarketEdge (
mvStart,
mvFinish
)
).cashAccountEdge();
double dblCashAccountAccumulationFinish = cae.accumulation();
double dblAssetNumeraireFinish = mvFinish.latentStateValue (equityLabel);
double dblBankSeniorFundingNumeraireFinish = mvFinish.dealer().seniorFundingReplicator();
double dblCounterPartyFundingNumeraireFinish = mvFinish.client().seniorFundingReplicator();
ReplicationPortfolioVertex rpvFinish = ReplicationPortfolioVertex.Standard (
-1. * dblDerivativeXVAValueDeltaFinish,
dblGainOnBankDefaultFinish / dblBankSeniorFundingNumeraireFinish,
dblGainOnCounterPartyDefaultFinish / dblCounterPartyFundingNumeraireFinish,
rpvStart.cashAccount() + dblCashAccountAccumulationFinish
);
System.out.println ("\t||" +
FormatUtil.FormatDouble (dblTime, 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (dblDerivativeXVAValueFinish, 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (dblAssetNumeraireFinish, 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (dblBankSeniorFundingNumeraireFinish, 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (dblCounterPartyFundingNumeraireFinish, 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (dblCollateralSchemeNumeraire, 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (rpvFinish.positionHoldings(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (rpvFinish.dealerSeniorNumeraireHoldings(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (rpvFinish.clientNumeraireHoldings(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (rpvFinish.cashAccount(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (dblCashAccountAccumulationFinish, 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (cae.assetAccumulation(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (cae.dealerAccumulation(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (cae.clientAccumulation(), 1, 6, 1.) + " ||"
);
return new EvolutionTrajectoryVertex (
dblTimeStart + dblTimeWidth,
rpvFinish,
new PositionGreekVertex (
dblDerivativeXVAValueFinish,
dblDerivativeXVAValueDeltaFinish,
dblDerivativeXVAValueGammaFinish,
agvStart.derivativeFairValue() * Math.exp (
-1. * dblTimeWidth * tc.csa().evolver().evaluator().drift().value (
new JumpDiffusionVertex (
dblTime,
dblCollateralSchemeNumeraire,
0.,
false
)
)
)
),
dblGainOnBankDefaultFinish,
dblGainOnCounterPartyDefaultFinish,
0.,
0.
);
}
public static void main (
final String[] astrArgs)
throws Exception
{
/* EnvManager.InitEnv ("");
String bank = "WFC";
int iNumVertex = 24;
String currency = "USD";
String counterParty = "BAC";
int iSimulationDuration = 365;
double[][] aadblCorrelationMatrix = new double[][] {
{1.00, 0.00, 0.20, 0.15, 0.05, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #0 ASSET NUMERAIRE
{0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #1 OVERNIGHT POLICY INDEX NUMERAIRE
{0.20, 0.00, 1.00, 0.13, 0.25, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #2 COLLATERAL SCHEME NUMERAIRE
{0.15, 0.00, 0.13, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #3 BANK HAZARD RATE
{0.05, 0.00, 0.25, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #4 BANK SENIOR FUNDING NUMERAIRE
{0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #5 BANK SENIOR RECOVERY RATE
{0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00}, // #6 BANK SUBORDINATE FUNDING NUMERAIRE
{0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00}, // #7 BANK SUBORDINATE RECOVERY RATE
{0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00}, // #8 COUNTER PARTY HAZARD RATE
{0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00}, // #9 COUNTER PARTY FUNDING NUMERAIRE
{0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00} // #10 COUNTER PARTY RECOVERY RATE
};
double dblAssetNumeraireDrift = 0.06;
double dblAssetNumeraireVolatility = 0.01;
double dblAssetNumeraireRepo = 0.03;
double dblAssetNumeraireDividend = 0.02;
double dblAssetNumeraireInitial = 1.;
double dblOvernightIndexNumeraireDrift = 0.0025;
double dblOvernightIndexNumeraireVolatility = 0.001;
double dblOvernightIndexNumeraireRepo = 0.0;
double dblCollateralSchemeNumeraireDrift = 0.01;
double dblCollateralSchemeNumeraireVolatility = 0.002;
double dblCollateralSchemeNumeraireRepo = 0.005;
double dblBankSeniorFundingNumeraireDrift = 0.03;
double dblBankSeniorFundingNumeraireVolatility = 0.002;
double dblBankSeniorFundingNumeraireRepo = 0.028;
double dblBankSubordinateFundingNumeraireDrift = 0.045;
double dblBankSubordinateFundingNumeraireVolatility = 0.002;
double dblBankSubordinateFundingNumeraireRepo = 0.028;
double dblCounterPartyFundingNumeraireDrift = 0.03;
double dblCounterPartyFundingNumeraireVolatility = 0.003;
double dblCounterPartyFundingNumeraireRepo = 0.028;
double dblBankHazardRateDrift = 0.00;
double dblBankHazardRateVolatility = 0.005;
double dblBankHazardRateInitial = 0.03;
double dblBankSeniorRecoveryRateDrift = 0.0;
double dblBankSeniorRecoveryRateVolatility = 0.0;
double dblBankSeniorRecoveryRateInitial = 0.45;
double dblBankSubordinateRecoveryRateDrift = 0.0;
double dblBankSubordinateRecoveryRateVolatility = 0.0;
double dblBankSubordinateRecoveryRateInitial = 0.25;
double dblCounterPartyHazardRateDrift = 0.00;
double dblCounterPartyHazardRateVolatility = 0.005;
double dblCounterPartyHazardRateInitial = 0.05;
double dblCounterPartyRecoveryRateDrift = 0.0;
double dblCounterPartyRecoveryRateVolatility = 0.0;
double dblCounterPartyRecoveryRateInitial = 0.30;
double dblTerminalXVADerivativeValue = 1.;
double dblSensitivityShiftFactor = 0.001;
EntityEquityLabel equityLabel = EntityEquityLabel.Standard (
"AAPL",
currency
);
PrimarySecurity tAsset = new PrimarySecurity (
"AAPL",
equityLabel,
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblAssetNumeraireDrift - dblAssetNumeraireDividend,
dblAssetNumeraireVolatility
)
),
dblAssetNumeraireRepo
);
PrimarySecurity tOvernightIndex = new PrimarySecurity (
currency + "_OVERNIGHT_ZERO",
OvernightLabel.Create (currency),
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblOvernightIndexNumeraireDrift,
dblOvernightIndexNumeraireVolatility
)
),
dblOvernightIndexNumeraireRepo
);
PrimarySecurity tCollateralScheme = new PrimarySecurity (
currency + "_CSA_ZERO",
CSALabel.ISDA (currency),
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblCollateralSchemeNumeraireDrift,
dblCollateralSchemeNumeraireVolatility
)
),
dblCollateralSchemeNumeraireRepo
);
PrimarySecurity tBankSeniorFunding = new PrimarySecurity (
bank + "_" + currency + "_SENIOR_ZERO",
EntityFundingLabel.Senior (
bank,
currency
),
new JumpDiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblBankSeniorFundingNumeraireDrift,
dblBankSeniorFundingNumeraireVolatility
),
HazardJumpEvaluator.Standard (
dblBankHazardRateInitial,
dblBankSeniorRecoveryRateInitial
)
),
dblBankSeniorFundingNumeraireRepo
);
PrimarySecurity tBankSubordinateFunding = new PrimarySecurity (
bank + "_" + currency + "_SUBORDINATE_ZERO",
EntityFundingLabel.Subordinate (
bank,
currency
),
new JumpDiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblBankSubordinateFundingNumeraireDrift,
dblBankSubordinateFundingNumeraireVolatility
),
HazardJumpEvaluator.Standard (
dblBankHazardRateInitial,
dblBankSubordinateRecoveryRateInitial
)
),
dblBankSubordinateFundingNumeraireRepo
);
PrimarySecurity tCounterPartyFunding = new PrimarySecurity (
counterParty + "_" + currency + "_SENIOR_ZERO",
EntityFundingLabel.Senior (
counterParty,
currency
),
new JumpDiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblCounterPartyFundingNumeraireDrift,
dblCounterPartyFundingNumeraireVolatility
),
HazardJumpEvaluator.Standard (
dblCounterPartyHazardRateInitial,
dblCounterPartyRecoveryRateInitial
)
),
dblCounterPartyFundingNumeraireRepo
);
JulianDate dtSpot = DateUtil.Today();
int iSpotDate = dtSpot.julian();
int aiVertexDate[] = VertexDateBuilder.EqualWidth (
iSpotDate,
iSpotDate + iSimulationDuration,
iNumVertex
);
List<PrimarySecurity> assetList = new ArrayList<PrimarySecurity>();
assetList.add (tAsset);
PrimarySecurityDynamicsContainer tc = new PrimarySecurityDynamicsContainer (
assetList,
tOvernightIndex,
tCollateralScheme,
tBankSeniorFunding,
tBankSubordinateFunding,
tCounterPartyFunding
);
MarketVertexGeneratorDeprecatione mvg = new MarketVertexGeneratorDeprecatione (
iSpotDate,
aiVertexDate,
tc,
new EntityDynamicsContainer (
new TerminalLatentState (
EntityHazardLabel.Standard (
bank,
currency
),
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblBankHazardRateDrift,
dblBankHazardRateVolatility
)
)
),
new TerminalLatentState (
EntityRecoveryLabel.Senior (
bank,
currency
),
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblBankSeniorRecoveryRateDrift,
dblBankSeniorRecoveryRateVolatility
)
)
),
new TerminalLatentState (
EntityRecoveryLabel.Subordinate (
bank,
currency
),
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblBankSubordinateRecoveryRateDrift,
dblBankSubordinateRecoveryRateVolatility
)
)
),
new TerminalLatentState (
EntityHazardLabel.Standard (
counterParty,
currency
),
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblCounterPartyHazardRateDrift,
dblCounterPartyHazardRateVolatility
)
)
),
new TerminalLatentState (
EntityRecoveryLabel.Senior (
counterParty,
currency
),
new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblCounterPartyRecoveryRateDrift,
dblCounterPartyRecoveryRateVolatility
)
)
)
)
);
LatentStateVertexContainer latentStateVertexContainer = new LatentStateVertexContainer();
latentStateVertexContainer.add (
EntityEquityLabel.Standard (
"AAPL",
currency
),
dblAssetNumeraireInitial
);
MarketVertex mvInitial = MarketVertex.Nodal (
dtSpot,
dblOvernightIndexNumeraireDrift,
1.,
dblCollateralSchemeNumeraireDrift,
1.,
new MarketVertexEntity (
1.,
dblBankHazardRateInitial,
dblBankSeniorRecoveryRateInitial,
dblBankSeniorFundingNumeraireDrift,
1.,
dblBankSubordinateRecoveryRateInitial,
dblBankSubordinateFundingNumeraireDrift,
1.
),
new MarketVertexEntity (
1.,
dblCounterPartyHazardRateInitial,
dblCounterPartyRecoveryRateInitial,
dblCounterPartyFundingNumeraireDrift,
1.,
Double.NaN,
Double.NaN,
Double.NaN
),
latentStateVertexContainer
);
MarketVertex[] aMV = MarketVertexArray (
mvg.marketVertex (
mvInitial,
Matrix.Transpose (
SequenceGenerator.GaussianJoint (
iNumVertex,
aadblCorrelationMatrix
)
)
)
);
double dblDerivativeValue = dblTerminalXVADerivativeValue;
double dblDerivativeXVAValue = dblTerminalXVADerivativeValue;
PDEEvolutionControl pdeec = new PDEEvolutionControl (
PDEEvolutionControl.CLOSEOUT_GREGORY_LI_TANG,
dblSensitivityShiftFactor
);
CloseOutBilateral cob = new CloseOutBilateral (
dblBankSeniorRecoveryRateInitial,
dblCounterPartyRecoveryRateInitial
);
TrajectoryEvolutionScheme tes = new TrajectoryEvolutionScheme (
tc,
pdeec
);
BurgardKjaerOperator bko = new BurgardKjaerOperator (
tc,
pdeec
);
PositionGreekVertex agvInitial = new PositionGreekVertex (
dblDerivativeXVAValue,
-1.,
0.,
dblDerivativeValue
);
double dblGainOnBankDefaultInitial = -1. * (dblDerivativeXVAValue - cob.dealerDefault
(dblDerivativeXVAValue));
double dblGainOnCounterPartyDefaultInitial = -1. * (dblDerivativeXVAValue - cob.clientDefault
(dblDerivativeXVAValue));
ReplicationPortfolioVertex rpvInitial = ReplicationPortfolioVertex.Standard (
1.,
dblGainOnBankDefaultInitial,
dblGainOnCounterPartyDefaultInitial,
0.
); */
EnvManager.InitEnv ("");
String dealer = "WFC";
String client = "BAC";
int vertexCount = 24;
String currency = "USD";
int simulationDuration = 365;
double dealerHazardRateInitial = 0.03;
double clientHazardRateInitial = 0.05;
double dealerSeniorRecoveryRateInitial = 0.40;
double clientRecoveryRateInitial = 0.40;
double[][] latentStateCorrelationMatrix = new double[][]
{
{1.00, 0.00, 0.20, 0.15, 0.05, 0.00, 0.00, 0.00, 0.00, 0.00}, // #0 DEALER HAZARD
{0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #1 DEALER SENIOR RECOVERY
{0.20, 0.00, 1.00, 0.13, 0.25, 0.00, 0.00, 0.00, 0.00, 0.00}, // #2 CLIENT HAZARD
{0.15, 0.00, 0.13, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #3 CLIENT RECOVERY
{0.05, 0.00, 0.25, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #4 OVERNIGHT REPLICATOR
{0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00}, // #5 CSA REPLICATOR
{0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00}, // #6 DEALER SENIOR FUNDING REPLICATOR
{0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00}, // #7 DEALER SUBORDINATE FUNDING REPLICATOR
{0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00}, // #8 CLIENT FUNDING REPLICATOR
{0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00}, // #9 EQUITY REPLICATOR
};
double dblTerminalXVADerivativeValue = 1.;
double dblSensitivityShiftFactor = 0.001;
JulianDate spotDateJulian = DateUtil.Today();
int spotDate = spotDateJulian.julian();
int[] eventVertexArray = VertexDateBuilder.EqualWidth (
spotDate,
spotDate + simulationDuration,
vertexCount
);
List<LatentStateLabel> latentStateLabelList = new ArrayList<LatentStateLabel>();
EntityEquityLabel equityLabel = EntityEquityLabel.Standard (
"AAPL",
currency
);
MarketVertexGenerator marketVertexGenerator = ConstructMarketVertexGenerator (
spotDateJulian,
eventVertexArray,
currency,
dealer,
client,
equityLabel,
latentStateLabelList
);
System.out.println ("marketVertexGenerator = " + marketVertexGenerator);
LatentStateVertexContainer latentStateVertexContainer = new LatentStateVertexContainer();
latentStateVertexContainer.add (
equityLabel,
1.
);
MarketVertex initialMarketVertex = MarketVertex.Epochal (
spotDateJulian,
1.000,
1.000,
dealerHazardRateInitial,
dealerSeniorRecoveryRateInitial,
dealerHazardRateInitial / (1 - dealerSeniorRecoveryRateInitial),
clientHazardRateInitial,
clientRecoveryRateInitial,
clientHazardRateInitial / (1 - clientRecoveryRateInitial),
latentStateVertexContainer
);
CorrelatedPathVertexDimension correlatedPathVertexDimension = new CorrelatedPathVertexDimension (
new RandomNumberGenerator(),
latentStateCorrelationMatrix,
vertexCount,
1,
true,
null
);
MarketVertex[] aMV = MarketVertexArray (
marketVertexGenerator.marketVertex (
initialMarketVertex,
LatentStateWeiner.FromUnitRandom (
latentStateLabelList,
Matrix.Transpose (correlatedPathVertexDimension.straightPathVertexRd().flatform())
)
)
);
System.out.println ("aMV = " + aMV);
double dblDerivativeValue = dblTerminalXVADerivativeValue;
double dblDerivativeXVAValue = dblTerminalXVADerivativeValue;
PDEEvolutionControl pdeec = new PDEEvolutionControl (
PDEEvolutionControl.CLOSEOUT_GREGORY_LI_TANG,
dblSensitivityShiftFactor
);
CloseOutBilateral cob = new CloseOutBilateral (
dealerSeniorRecoveryRateInitial,
clientRecoveryRateInitial
);
TrajectoryEvolutionScheme tes = new TrajectoryEvolutionScheme (
marketVertexGenerator.primarySecurityDynamicsContainer(),
pdeec
);
BurgardKjaerOperator bko = new BurgardKjaerOperator (
marketVertexGenerator.primarySecurityDynamicsContainer(),
pdeec
);
PositionGreekVertex agvInitial = new PositionGreekVertex (
dblDerivativeXVAValue,
-1.,
0.,
dblDerivativeValue
);
double dblGainOnBankDefaultInitial = -1. * (dblDerivativeXVAValue - cob.dealerDefault
(dblDerivativeXVAValue));
double dblGainOnCounterPartyDefaultInitial = -1. * (dblDerivativeXVAValue - cob.clientDefault
(dblDerivativeXVAValue));
ReplicationPortfolioVertex rpvInitial = ReplicationPortfolioVertex.Standard (
1.,
dblGainOnBankDefaultInitial,
dblGainOnCounterPartyDefaultInitial,
0.
);
System.out.println();
System.out.println ("\t||-----------------------------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t|| BILATERAL XVA EVOLVER - BURGARD & KJAER (2011) REPLICATION PORTFOLIO EVOLUTION ||");
System.out.println ("\t||-----------------------------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t|| L -> R: ||");
System.out.println ("\t|| - Time ||");
System.out.println ("\t|| - Derivative XVA Value ||");
System.out.println ("\t|| - Asset Price Realization ||");
System.out.println ("\t|| - Realization of the Zero Coupon Bank Bond Price ||");
System.out.println ("\t|| - Realization of the Zero Coupon Counter Party Bond Price ||");
System.out.println ("\t|| - Realization of the Zero Coupon Collateral Bond Price ||");
System.out.println ("\t|| - Derivative XVA Asset Replication Units ||");
System.out.println ("\t|| - Derivative XVA Value Bank Bond Replication Units ||");
System.out.println ("\t|| - Derivative XVA Value Counter Party Bond Replication Units ||");
System.out.println ("\t|| - Derivative XVA Value Cash Account Replication Units ||");
System.out.println ("\t|| - Derivative Cash Account Accumulation Component ||");
System.out.println ("\t|| - Asset Cash Account Accumulation Component ||");
System.out.println ("\t|| - Bank Cash Account Accumulation Component ||");
System.out.println ("\t|| - Counter Party Cash Account Accumulation Component ||");
System.out.println ("\t||-----------------------------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t||" +
FormatUtil.FormatDouble (1., 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (agvInitial.derivativeXVAValue(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (aMV[aMV.length - 1].latentStateValue (equityLabel), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (1., 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (1., 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (1., 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (rpvInitial.positionHoldings(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (rpvInitial.dealerSeniorNumeraireHoldings(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (rpvInitial.clientNumeraireHoldings(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (rpvInitial.cashAccount(), 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (0., 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (0., 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (0., 1, 6, 1.) + " | " +
FormatUtil.FormatDouble (0., 1, 6, 1.) + " ||"
);
EvolutionTrajectoryVertex etv = new EvolutionTrajectoryVertex (
1.,
rpvInitial,
agvInitial,
dblGainOnBankDefaultInitial,
dblGainOnCounterPartyDefaultInitial,
0.,
0.
);
for (int i = vertexCount - 1; i >= 0; --i)
etv = RunStep (
tes,
bko,
etv,
aMV[i + 1],
aMV[i],
equityLabel
);
System.out.println ("\t||-----------------------------------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println();
EnvManager.TerminateEnv();
}
}