CSAImpliedMeasureDifference.java
package org.drip.sample.piterbarg2010;
import java.util.Map;
import org.drip.analytics.date.*;
import org.drip.exposure.csadynamics.*;
import org.drip.function.r1tor1.FlatUnivariate;
import org.drip.measure.dynamics.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.param.valuation.ValuationParams;
import org.drip.pricer.option.BlackScholesAlgorithm;
import org.drip.product.option.EuropeanCallPut;
import org.drip.service.env.EnvManager;
import org.drip.service.template.LatentMarketStateBuilder;
import org.drip.state.discount.MergedDiscountForwardCurve;
/*
* -*- 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.
*/
/**
* CSAImpliedMeasureDifference compares the Differences between the CSA and the non-CSA Implied Distribution,
* expressed in Implied Volatilities across Strikes, and across Correlations. The References are:
*
* - Barden, P. (2009): Equity Forward Prices in the Presence of Funding Spreads, ICBI Conference, Rome.
*
* - Burgard, C., and M. Kjaer (2009): Modeling and successful Management of Credit Counter-party Risk of
* Derivative Portfolios, ICBI Conference, Rome.
*
* - Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk, Risk 20 (2) 86-90.
*
* - Johannes, M., and S. Sundaresan (2007): Pricing Collateralized Swaps, Journal of Finance 62 383-410.
*
* - Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing, Risk
* 21 (2) 97-102.
*
* @author Lakshmi Krishnamurthy
*/
public class CSAImpliedMeasureDifference {
private static final MergedDiscountForwardCurve OvernightCurve (
final String strCurrency,
final JulianDate dtSpot)
throws Exception
{
String[] astrDepositMaturityTenor = new String[] {
"1D",
// "2D",
"3D"
};
double[] adblDepositQuote = new double[] {
0.0004, // 1D
// 0.0004, // 2D
0.0004 // 3D
};
String[] astrShortEndOISMaturityTenor = new String[] {
"1W",
"2W",
"3W",
"1M"
};
double[] adblShortEndOISQuote = new double[] {
0.00070, // 1W
0.00069, // 2W
0.00078, // 3W
0.00074 // 1M
};
String[] astrOISFuturesEffectiveTenor = new String[] {
"1M",
"2M",
"3M",
"4M",
"5M"
};
String[] astrOISFuturesMaturityTenor = new String[] {
"1M",
"1M",
"1M",
"1M",
"1M"
};
double[] adblOISFuturesQuote = new double[] {
0.00046, // 1M x 1M
0.00016, // 2M x 1M
-0.00007, // 3M x 1M
-0.00013, // 4M x 1M
-0.00014 // 5M x 1M
};
String[] astrLongEndOISMaturityTenor = new String[] {
"15M",
"18M",
"21M",
"02Y",
"03Y",
"04Y",
"05Y",
"06Y",
"07Y",
"08Y",
"09Y",
"10Y",
"11Y",
"12Y",
"15Y",
"20Y",
"25Y",
"30Y"
};
double[] adblLongEndOISQuote = new double[] {
0.00002, // 15M
0.00008, // 18M
0.00021, // 21M
0.00036, // 2Y
0.00127, // 3Y
0.00274, // 4Y
0.00456, // 5Y
0.00647, // 6Y
0.00827, // 7Y
0.00996, // 8Y
0.01147, // 9Y
0.01280, // 10Y
0.01404, // 11Y
0.01516, // 12Y
0.01764, // 15Y
0.01939, // 20Y
0.02003, // 25Y
0.02038 // 30Y
};
return LatentMarketStateBuilder.SmoothOvernightCurve (
dtSpot,
strCurrency,
astrDepositMaturityTenor,
adblDepositQuote,
"Rate",
astrShortEndOISMaturityTenor,
adblShortEndOISQuote,
"SwapRate",
astrOISFuturesEffectiveTenor,
astrOISFuturesMaturityTenor,
adblOISFuturesQuote,
"SwapRate",
astrLongEndOISMaturityTenor,
adblLongEndOISQuote,
"SwapRate"
);
}
public static final void main (
final String[] astrArgs)
throws Exception
{
EnvManager.InitEnv ("");
String strTenor = "10Y";
double dblCSAForward = 100.;
double dblFundingSpreadVolatility = 0.015;
double dblFundingSpreadMeanReversionRate = 0.05;
String strCurrency = "USD";
JulianDate dtSpot = DateUtil.CreateFromYMD (
2017,
DateUtil.DECEMBER,
21
);
double[] adblCorrelation = new double[] {
-0.30,
-0.10,
0.00,
0.10
};
double[] adblStrike = new double[] {
50.,
60.,
70.,
80.,
90.,
100.,
110.,
120.,
130.,
140.,
150.
};
double[] adblCSAImpliedVolatility = new double[] {
0.30,
0.30,
0.30,
0.30,
0.30,
0.30,
0.30,
0.30,
0.30,
0.30,
0.30
};
double[][] aadblNoCSAForward = new double[adblCorrelation.length][adblStrike.length];
double[][] aadblMeasureShiftScale = new double[adblCorrelation.length][adblStrike.length];
DiffusionEvaluatorMeanReversion demrFundingSpread = DiffusionEvaluatorMeanReversion.Standard (
dblFundingSpreadMeanReversionRate,
0.,
dblFundingSpreadVolatility
);
System.out.println ();
System.out.println ("\t||----------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t|| PROBABILITY MEASURE DISTRIBUTION SHIFT ||");
System.out.println ("\t||----------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t|| L -> R : ||");
System.out.println ("\t|| - Correlation ||");
System.out.println ("\t|| - Adjustments for Strikes in unit of 10, from 50 to 150 ||");
System.out.println ("\t||----------------------------------------------------------------------------------------------------------------------||");
for (int j = 0; j < adblCorrelation.length; ++j) {
String strDump = "\t|| " + FormatUtil.FormatDouble (adblCorrelation[j], 2, 0, 100.) + "% => ";
for (int i = 0; i < adblStrike.length; ++i) {
DiffusionEvaluatorLogarithmic delUnderlying = DiffusionEvaluatorLogarithmic.Standard (
0.,
adblCSAImpliedVolatility[i]
);
FundingBasisEvolver fbe = new FundingBasisEvolver (
delUnderlying,
demrFundingSpread,
adblCorrelation[j]
);
aadblNoCSAForward[j][i] = dblCSAForward * fbe.CSANoCSARatio (strTenor);
NumeraireInducedMeasureShift nims = new NumeraireInducedMeasureShift (
dblCSAForward,
aadblNoCSAForward[j][i],
dblCSAForward * dblCSAForward * adblCSAImpliedVolatility[i] * adblCSAImpliedVolatility[i]
);
aadblMeasureShiftScale[j][i] = nims.densityRescale (adblStrike[i]);
strDump = strDump + " " + FormatUtil.FormatDouble (aadblMeasureShiftScale[j][i], 1, 4, 1.) + " |";
}
System.out.println (strDump + "|");;
}
System.out.println ("\t||----------------------------------------------------------------------------------------------------------------------||");
System.out.println ();
MergedDiscountForwardCurve dcOvernight = OvernightCurve (
strCurrency,
dtSpot
);
JulianDate dtMaturity = dtSpot.addTenor (strTenor);
ValuationParams valParams = new ValuationParams (
dtSpot,
dtSpot,
strCurrency
);
double[] adblPrice = new double[adblStrike.length];
EuropeanCallPut[] aECP = new EuropeanCallPut[adblStrike.length];
System.out.println ("\t||---------------------------------------------------------------------------------------------------------------------------||");
String strDump = "\t|| CSA ATM Option Price => ";
for (int i = 0; i < adblStrike.length; ++i) {
aECP[i] = new EuropeanCallPut (
dtMaturity,
adblStrike[i]
);
Map<String, Double> mapOptionCalc = aECP[i].value (
valParams,
dblCSAForward,
true,
dcOvernight,
new FlatUnivariate (adblCSAImpliedVolatility[i]),
new BlackScholesAlgorithm()
);
adblPrice[i] = mapOptionCalc.get ("CallPrice");
strDump = strDump + FormatUtil.FormatDouble (adblPrice[i], 2, 2, 1.) + " |";
}
System.out.println (strDump + "|");
System.out.println ("\t||---------------------------------------------------------------------------------------------------------------------------||");
System.out.println ();
System.out.println ("\t||-----------------------------------------------------------------------------------------------------------||");
System.out.println ("\t|| CSA CONVEXITY ADJUSTMENT IMPLIED VOLATILITY ||");
System.out.println ("\t||-----------------------------------------------------------------------------------------------------------||");
System.out.println ("\t|| L -> R : ||");
System.out.println ("\t|| - Implied Volatility (%) ||");
System.out.println ("\t|| - Adjustments for Strikes in unit of 10, from 50 to 150 ||");
System.out.println ("\t||-----------------------------------------------------------------------------------------------------------||");
for (int j = 0; j < adblCorrelation.length; ++j) {
strDump = "\t|| " + FormatUtil.FormatDouble (adblCorrelation[j], 2, 0, 100.) + "% => ";
for (int i = 0; i < adblStrike.length; ++i) {
double dblReimpliedVolatility = aECP[i].implyVolatilityFromCallPrice (
valParams,
aadblNoCSAForward[j][i],
true,
dcOvernight,
adblPrice[i]
);
strDump = strDump + FormatUtil.FormatDouble (dblReimpliedVolatility, 2, 2, 100.) + "% |";
}
System.out.println (strDump + "|");
}
System.out.println ("\t||-----------------------------------------------------------------------------------------------------------||");
System.out.println ();
}
}