ExposurePathLocalVolatility.java
package org.drip.sample.pykhtin2009;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import org.drip.analytics.date.DateUtil;
import org.drip.analytics.date.JulianDate;
import org.drip.exposure.csatimeline.AndersenPykhtinSokolLag;
import org.drip.exposure.evolver.EntityDynamicsContainer;
import org.drip.exposure.evolver.LatentStateDynamicsContainer;
import org.drip.exposure.evolver.LatentStateVertexContainer;
import org.drip.exposure.evolver.PrimarySecurity;
import org.drip.exposure.evolver.PrimarySecurityDynamicsContainer;
import org.drip.exposure.evolver.TerminalLatentState;
import org.drip.exposure.generator.NumeraireMPoR;
import org.drip.exposure.mpor.PathVariationMarginTrajectoryEstimator;
import org.drip.exposure.regression.LocalVolatilityGenerationControl;
import org.drip.exposure.regression.PykhtinPillarDynamics;
import org.drip.exposure.universe.LatentStateWeiner;
import org.drip.exposure.universe.MarketPath;
import org.drip.exposure.universe.MarketVertex;
import org.drip.exposure.universe.MarketVertexGenerator;
import org.drip.function.definition.R1ToR1;
import org.drip.measure.crng.RandomNumberGenerator;
import org.drip.measure.discrete.CorrelatedPathVertexDimension;
import org.drip.measure.dynamics.DiffusionEvaluatorLinear;
import org.drip.measure.dynamics.DiffusionEvaluatorLogarithmic;
import org.drip.measure.dynamics.HazardJumpEvaluator;
import org.drip.measure.process.DiffusionEvolver;
import org.drip.measure.process.JumpDiffusionEvolver;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.linearalgebra.Matrix;
import org.drip.service.env.EnvManager;
import org.drip.state.identifier.CSALabel;
import org.drip.state.identifier.EntityEquityLabel;
import org.drip.state.identifier.EntityFundingLabel;
import org.drip.state.identifier.EntityHazardLabel;
import org.drip.state.identifier.EntityRecoveryLabel;
import org.drip.state.identifier.LatentStateLabel;
import org.drip.state.identifier.OvernightLabel;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2018 Lakshmi Krishnamurthy
*
* This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
* libraries targeting analysts and developers
* https://lakshmidrip.github.io/DRIP/
*
* DRIP is composed of four main libraries:
*
* - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
* - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
* - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
* - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
*
* - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
* Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
* Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
* Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
* Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
*
* - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
* Incorporator, Holdings Constraint, and Transaction Costs.
*
* - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
*
* - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
*
* 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.
*/
/**
* ExposurePathLocalVolatility estimates the Path-wise Local Volatility Realizations using the Pykhtin (2009)
* Scheme. The References are:
*
* - Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Re-thinking Margin Period of Risk,
* https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2902737, eSSRN.
*
* - Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Credit Exposure in the Presence of Initial Margin,
* https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2806156, eSSRN.
*
* - Albanese, C., and L. Andersen (2014): Accounting for OTC Derivatives: Funding Adjustments and the
* Re-Hypothecation Option, eSSRN, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2482955.
*
* - Burgard, C., and M. Kjaer (2017): Derivatives Funding, Netting, and Accounting, eSSRN,
* https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2534011.
*
* - Pykhtin, M. (2009): Modeling Counter-party Credit Exposure in the Presence of Margin Agreements,
* http://www.risk-europe.com/protected/michael-pykhtin.pdf.
*
* @author Lakshmi Krishnamurthy
*/
public class ExposurePathLocalVolatility
{
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 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 PrimarySecurityDynamicsContainer PrimarySecurityEvolver (
final String currency,
final String dealer,
final String client,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
return new PrimarySecurityDynamicsContainer (
null,
OvernightReplicator (
currency,
latentStateLabelList
),
CSAReplicator (
currency,
latentStateLabelList
),
DealerSeniorFundingReplicator (
currency,
dealer,
latentStateLabelList
),
DealerSubordinateFundingReplicator (
currency,
dealer,
latentStateLabelList
),
ClientFundingReplicator (
currency,
client,
latentStateLabelList
)
);
}
private static final LatentStateDynamicsContainer LatentStateEvolver (
final EntityEquityLabel equityLabel,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
double equityNumeraireDrift = 0.05;
double equityNumeraireVolatility = 0.10;
latentStateLabelList.add (equityLabel);
LatentStateDynamicsContainer latentStateDynamicsContainer = new LatentStateDynamicsContainer();
latentStateDynamicsContainer.addEntityEquity (
new TerminalLatentState (
equityLabel,
new DiffusionEvolver (
DiffusionEvaluatorLinear.Standard (
equityNumeraireDrift,
equityNumeraireVolatility
)
)
)
);
return latentStateDynamicsContainer;
}
private static final MarketVertexGenerator ConstructMarketVertexGenerator (
final JulianDate spotDate,
final String exposureSamplingTenor,
final int exposureSamplingNodeCount,
final String currency,
final String dealer,
final String client,
final EntityEquityLabel equityLabel,
final List<LatentStateLabel> latentStateLabelList)
throws Exception
{
JulianDate terminationDate = spotDate;
int[] eventVertexArray = new int[exposureSamplingNodeCount];
for (int i = 0; i < exposureSamplingNodeCount; ++i)
{
terminationDate = terminationDate.addTenor (exposureSamplingTenor);
eventVertexArray[i] = terminationDate.julian();
}
return new MarketVertexGenerator (
spotDate.julian(),
eventVertexArray,
EntityEvolver (
currency,
dealer,
client,
latentStateLabelList
),
PrimarySecurityEvolver (
currency,
dealer,
client,
latentStateLabelList
),
LatentStateEvolver (
equityLabel,
latentStateLabelList
)
);
}
public static final void main (
final String[] args)
throws Exception
{
EnvManager.InitEnv ("");
JulianDate spotDate = DateUtil.CreateFromYMD (
2018,
DateUtil.APRIL,
19
);
int pathCount = 10000;
String exposurePeriodTenor = "6M";
int exposurePeriodCount = 15;
String currency = "USD";
String dealer = "NOM";
String client = "SSGA";
double[][] correlationMatrix = 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 OTC FIX FLOAT REPLICATOR
};
String referenceEntity = "HYG";
double equityNotional = 10.;
LocalVolatilityGenerationControl localVolatilityGenerationControl =
LocalVolatilityGenerationControl.Standard (pathCount);
EntityEquityLabel equityLabel = EntityEquityLabel.Standard (
referenceEntity,
currency
);
NumeraireMPoR numeraireMPoR = new NumeraireMPoR (
equityLabel,
equityNotional
);
List<LatentStateLabel> latentStateLabelList = new ArrayList<LatentStateLabel>();
MarketVertexGenerator marketVertexGenerator = ConstructMarketVertexGenerator (
spotDate,
exposurePeriodTenor,
exposurePeriodCount,
currency,
dealer,
client,
equityLabel,
latentStateLabelList
);
LatentStateVertexContainer latentStateVertexContainer = new LatentStateVertexContainer();
latentStateVertexContainer.add (
equityLabel,
10.
);
MarketVertex initialMarketVertex = MarketVertex.Epochal (
spotDate,
1.000, // dblOvernightNumeraireInitial
1.000, // dblCSANumeraire
0.015, // dblBankHazardRate
0.400, // dblBankRecoveryRate
0.015 / (1 - 0.40), // dblBankFundingSpread
0.030, // dblCounterPartyHazardRate
0.300, // dblCounterPartyRecoveryRate
0.030 / (1 - 0.30), // dblCounterPartyFundingSpread
latentStateVertexContainer
);
AndersenPykhtinSokolLag andersenPykhtinSokolLag = AndersenPykhtinSokolLag.ClassicalMinus();
CorrelatedPathVertexDimension correlatedPathVertexDimension = new CorrelatedPathVertexDimension (
new RandomNumberGenerator(),
correlationMatrix,
exposurePeriodCount,
1,
true,
null
);
JulianDate exposureDate = spotDate;
int[] exposureDateArray = new int[exposurePeriodCount + 1];
R1ToR1[] localVolatilityR1ToR1Array = new R1ToR1[exposurePeriodCount + 1];
double[][] pathExposureArray = new double[exposurePeriodCount + 1][pathCount];
for (int i = 0; i <= exposurePeriodCount; ++i)
{
exposureDateArray[i] = exposureDate.julian();
exposureDate = exposureDate.addTenor (exposurePeriodTenor);
}
for (int pathIndex = 0; pathIndex < pathCount; ++pathIndex)
{
MarketPath marketPath = new MarketPath (
marketVertexGenerator.marketVertex (
initialMarketVertex,
LatentStateWeiner.FromUnitRandom (
latentStateLabelList,
Matrix.Transpose (correlatedPathVertexDimension.straightPathVertexRd().flatform())
)
)
);
PathVariationMarginTrajectoryEstimator variationMarginTradeTrajectoryEstimator =
PathVariationMarginTrajectoryEstimator.Standard (
exposureDateArray,
currency,
numeraireMPoR,
marketPath,
andersenPykhtinSokolLag
);
Map<Integer, Double> variationMarginEstimateTrajectory =
variationMarginTradeTrajectoryEstimator.variationMarginEstimateTrajectory();
int exposureDateIndex = 0;
for (Map.Entry<Integer, Double> variationMarginEstimateTrajectoryEntry :
variationMarginEstimateTrajectory.entrySet())
{
pathExposureArray[exposureDateIndex++][pathIndex] =
variationMarginEstimateTrajectoryEntry.getValue();
}
}
System.out.println ("\t||------------------------------------------------------------------------------------------------------------");
System.out.println ("\t|| Sorted Exposure Node Realizations");
System.out.println ("\t||------------------------------------------------------------------------------------------------------------");
System.out.println ("\t|| ");
System.out.println ("\t|| L -> R: ");
System.out.println ("\t|| - Exposure Date ");
System.out.println ("\t|| - The Spot/Forward Exposures ");
System.out.println ("\t||------------------------------------------------------------------------------------------------------------");
for (int exposureDateIndex = 0; exposureDateIndex < exposurePeriodCount; ++exposureDateIndex)
{
String strDump = "\t|| " + new JulianDate (exposureDateArray[exposureDateIndex]) + " => ";
for (int pathIndex = 0; pathIndex < pathCount; ++pathIndex)
{
strDump += FormatUtil.FormatDouble (pathExposureArray[exposureDateIndex][pathIndex], 3, 1, 1.) + " | ";
}
System.out.println (strDump);
}
System.out.println ("\t||------------------------------------------------------------------------------------------------------------");
System.out.println();
for (int exposureDateIndex = 0; exposureDateIndex < exposurePeriodCount; ++exposureDateIndex)
{
PykhtinPillarDynamics vertexRealization = PykhtinPillarDynamics.Standard
(pathExposureArray [exposureDateIndex]);
localVolatilityR1ToR1Array[exposureDateIndex] = null == vertexRealization ? null :
vertexRealization.localVolatilityR1ToR1 (localVolatilityGenerationControl);
}
System.out.println ("\t||------------------------------------------------------------------------------------------------------------");
System.out.println ("\t|| EXPOSURE DATE LOCAL VOLATILITY ");
System.out.println ("\t||------------------------------------------------------------------------------------------------------------");
System.out.println ("\t|| ");
System.out.println ("\t|| L -> R: ");
System.out.println ("\t|| - Simulation Path Number ");
System.out.println ("\t|| - The Spot/Forward Dates ");
System.out.println ("\t||------------------------------------------------------------------------------------------------------------");
for (int pathIndex = 0; pathIndex < pathCount; ++pathIndex)
{
String strDump = "\t|| " + FormatUtil.FormatDouble (pathIndex, 5, 0, 1.) + " => ";
for (int exposureDateIndex = 0; exposureDateIndex < exposurePeriodCount; ++exposureDateIndex)
{
strDump += FormatUtil.FormatDouble (
null == localVolatilityR1ToR1Array[exposureDateIndex] ? 0. :
localVolatilityR1ToR1Array[exposureDateIndex].evaluate (
pathExposureArray [exposureDateIndex][pathIndex]
), 1, 6, 1.
) + " | ";
}
System.out.println (strDump);
}
System.out.println ("\t||------------------------------------------------------------------------------------------------------------");
EnvManager.TerminateEnv();
}
}