R1JointDiffusion.java
package org.drip.sample.numeraire;
import org.drip.measure.discrete.SequenceGenerator;
import org.drip.measure.dynamics.DiffusionEvaluatorLogarithmic;
import org.drip.measure.process.DiffusionEvolver;
import org.drip.measure.realization.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.linearalgebra.Matrix;
import org.drip.service.env.EnvManager;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 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.
*/
/**
* R1JointDiffusion demonstrates the Joint Evolution of R^1 Diffusion Variates - the Continuous Asset, the
* Collateral, the Bank, and the Counter-Party Numeraires involved in the Dynamic XVA Replication Portfolio
* of the Burgard and Kjaer (2011) Methodology. The References are:
*
* - Burgard, C., and M. Kjaer (2014): PDE Representations of Derivatives with Bilateral Counter-party Risk
* and Funding Costs, Journal of Credit Risk, 7 (3) 1-19.
*
* - Cesari, G., J. Aquilina, N. Charpillon, X. Filipovic, G. Lee, and L. Manda (2009): Modeling, Pricing,
* and Hedging Counter-party Credit Exposure - A Technical Guide, Springer Finance, New York.
*
* - Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk, Risk 20 (2) 86-90.
*
* - Li, B., and Y. Tang (2007): Quantitative Analysis, Derivatives Modeling, and Trading Strategies in the
* Presence of Counter-party Credit Risk for the Fixed Income Market, World Scientific Publishing,
* Singapore.
*
* - Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing, Risk
* 21 (2) 97-102.
*
* @author Lakshmi Krishnamurthy
*/
public class R1JointDiffusion {
private static final double[][] NumeraireSequence (
final int iCount,
final double[][] aadblCorrelation,
final String strHeader)
throws Exception
{
double[][] aadblGaussianJoint = SequenceGenerator.GaussianJoint (
iCount,
aadblCorrelation
);
System.out.println();
System.out.println ("\t||----------------------------------------------------||");
System.out.println (strHeader);
System.out.println ("\t||----------------------------------------------------||");
for (int i = 0; i < iCount; ++i) {
String strDump = "\t||" + FormatUtil.FormatDouble (i, 2, 0, 1.) + " |";
for (int j = 0; j < aadblCorrelation.length; ++j)
strDump = strDump + " " + FormatUtil.FormatDouble (aadblGaussianJoint[i][j], 1, 6, 1.) + " |";
System.out.println (strDump + "|");
}
System.out.println ("\t||----------------------------------------------------||");
System.out.println();
return Matrix.Transpose (aadblGaussianJoint);
}
public static final void main (
final String[] astrArgs)
throws Exception
{
EnvManager.InitEnv ("");
double dblTimeWidth = 1. / 24.;
double dblTime = 1.;
double[][] aadblCorrelation = new double[][] {
{1.00, 0.20, 0.15, 0.05}, // #0 ASSET
{0.20, 1.00, 0.13, 0.25}, // #1 COLLATERAL
{0.15, 0.13, 1.00, 0.00}, // #2 BANK
{0.05, 0.25, 0.00, 1.00} // #3 COUNTER PARTY
};
double dblAssetDrift = 0.06;
double dblAssetVolatility = 0.15;
double dblTerminalBankNumeraire = 1.;
double dblTerminalAssetNumeraire = 1.;
double dblTerminalCollateralNumeraire = 1.;
int iNumTimeStep = (int) (dblTime / dblTimeWidth);
double[] adblTimeWidth = new double[iNumTimeStep];
for (int i = 0; i < iNumTimeStep; ++i)
adblTimeWidth[i] = dblTimeWidth;
DiffusionEvolver meAsset = new DiffusionEvolver (
DiffusionEvaluatorLogarithmic.Standard (
dblAssetDrift,
dblAssetVolatility
)
);
double[][] aadblNumeraireTimeSeries = NumeraireSequence (
iNumTimeStep,
aadblCorrelation,
"\t|| ASSET, COLLATERAL, BANK, COUNTER PARTY REALIZATION ||"
);
JumpDiffusionEdge[] aR1AssetLR = meAsset.incrementSequence (
new JumpDiffusionVertex (
dblTime,
dblTerminalAssetNumeraire,
0.,
false
),
JumpDiffusionEdgeUnit.Diffusion (
adblTimeWidth,
aadblNumeraireTimeSeries[0]
),
-1. * dblTimeWidth
);
JumpDiffusionEdge[] aR1CollateralLR = meAsset.incrementSequence (
new JumpDiffusionVertex (
dblTime,
dblTerminalCollateralNumeraire,
0.,
false
),
JumpDiffusionEdgeUnit.Diffusion (
adblTimeWidth,
aadblNumeraireTimeSeries[1]
),
-1. * dblTimeWidth
);
JumpDiffusionEdge[] aR1BankLR = meAsset.incrementSequence (
new JumpDiffusionVertex (
dblTime,
dblTerminalBankNumeraire,
0.,
false
),
JumpDiffusionEdgeUnit.Diffusion (
adblTimeWidth,
aadblNumeraireTimeSeries[2]
),
-1. * dblTimeWidth
);
JumpDiffusionEdge[] aR1CounterPartyLR = meAsset.incrementSequence (
new JumpDiffusionVertex (
dblTime,
dblTerminalBankNumeraire,
0.,
false
),
JumpDiffusionEdgeUnit.Diffusion (
adblTimeWidth,
aadblNumeraireTimeSeries[3]
),
-1. * dblTimeWidth
);
System.out.println();
System.out.println("\t||----------------------------------------------------------------------------------------------------------------------------------||");
System.out.println("\t|| BURGARD & KJAER (2011) CORRELATED JOINT ASSET/COLLATERAL/BANK/COUNTER-PARTY NUMERAIRE EVOLUTION ||");
System.out.println("\t||----------------------------------------------------------------------------------------------------------------------------------||");
System.out.println("\t|| L -> R: ||");
System.out.println("\t|| - Time ||");
System.out.println("\t|| - Asset Numeraire Finish Value ||");
System.out.println("\t|| - Asset Numeraire Start Value ||");
System.out.println("\t|| - Asset Numeraire Continuous Wander Realization ||");
System.out.println("\t|| - Collateral Numeraire Finish Value ||");
System.out.println("\t|| - Collateral Numeraire Start Value ||");
System.out.println("\t|| - Collateral Numeraire Continuous Wander Realization ||");
System.out.println("\t|| - Bank Numeraire Finish Value ||");
System.out.println("\t|| - Bank Numeraire Start Value ||");
System.out.println("\t|| - Bank Numeraire Continuous Wander Realization ||");
System.out.println("\t|| - Counter-Party Numeraire Finish Value ||");
System.out.println("\t|| - Counter-Party Numeraire Start Value ||");
System.out.println("\t|| - Counter-Party Numeraire Continuous Wander Realization ||");
System.out.println("\t||----------------------------------------------------------------------------------------------------------------------------------||");
for (int i = 0; i < iNumTimeStep; ++i) {
dblTime = dblTime - dblTimeWidth;
System.out.println (
"\t|| " +
FormatUtil.FormatDouble (dblTime, 1, 4, 1.) + " => " +
FormatUtil.FormatDouble (aR1AssetLR[i].start(), 1, 4, 1.) + " | " +
FormatUtil.FormatDouble (aR1AssetLR[i].finish(), 1, 4, 1.) + " | " +
FormatUtil.FormatDouble (aR1AssetLR[i].diffusionWander(), 1, 4, 1.) + " ||" +
FormatUtil.FormatDouble (aR1CollateralLR[i].start(), 1, 4, 1.) + " | " +
FormatUtil.FormatDouble (aR1CollateralLR[i].finish(), 1, 4, 1.) + " | " +
FormatUtil.FormatDouble (aR1CollateralLR[i].diffusionWander(), 1, 4, 1.) + " ||" +
FormatUtil.FormatDouble (aR1BankLR[i].start(), 1, 4, 1.) + " | " +
FormatUtil.FormatDouble (aR1BankLR[i].finish(), 1, 4, 1.) + " | " +
FormatUtil.FormatDouble (aR1BankLR[i].diffusionWander(), 1, 4, 1.) + " ||" +
FormatUtil.FormatDouble (aR1CounterPartyLR[i].start(), 1, 4, 1.) + " | " +
FormatUtil.FormatDouble (aR1CounterPartyLR[i].finish(), 1, 4, 1.) + " | " +
FormatUtil.FormatDouble (aR1CounterPartyLR[i].diffusionWander(), 1, 4, 1.) + " ||"
);
}
System.out.println("\t||----------------------------------------------------------------------------------------------------------------------------------||");
System.out.println();
}
}