ModelMTMDistribution11a.java
package org.drip.sample.anfuso2017;
import org.drip.measure.gaussian.R1UnivariateNormal;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.validation.evidence.Sample;
import org.drip.validation.hypothesis.ProbabilityIntegralTransform;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 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>ModelMTMDistribution11a</i> illustrates the Model MTM Distributions laid out in Table 11a of Anfuso,
* Karyampas, and Nawroth (2017).
*
* <br><br>
* <ul>
* <li>
* Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
* Back-testing Credit Exposure Models
* https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
* </li>
* <li>
* Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
* Applications to Financial Risk Management, International Economic Review 39 (4) 863-883
* </li>
* <li>
* Kenyon, C., and R. Stamm (2012): Discounting, LIBOR, CVA, and Funding: Interest Rate and Credit
* Pricing, Palgrave Macmillan
* </li>
* <li>
* Wikipedia (2018): Probability Integral Transform
* https://en.wikipedia.org/wiki/Probability_integral_transform
* </li>
* <li>
* Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation 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/anfuso2017/README.md">Anfuso, Karyampas, and Nawroth (2013) Replications</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class ModelMTMDistribution11a
{
private static final double UnivariateRandom (
final double mean,
final double sigma)
throws Exception
{
return new R1UnivariateNormal (
mean,
sigma
).random();
}
private static final Sample GenerateSample (
final double mean,
final double sigma,
final int drawCount)
throws Exception
{
double[] univariateRandomArray = new double[drawCount];
for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
{
univariateRandomArray[drawIndex] = UnivariateRandom (
mean,
sigma
);
}
return new Sample (univariateRandomArray);
}
private static final void ProbabilityPlot (
final ProbabilityIntegralTransform pitTooHighVolatility,
final ProbabilityIntegralTransform pitCorrectVolatility,
final ProbabilityIntegralTransform pitTooLowVolatility,
final double xLeft,
final double xRight,
final double xWidth)
throws Exception
{
double leftProbabilityTooHighVolatility = 0.;
double leftProbabilityCorrectVolatility = 0.;
double leftProbabilityTooLowVolatility = 0.;
for (double x = xLeft; x <= xRight; x += xWidth)
{
double probabilityTooHighVolatility = pitTooHighVolatility.pValue (x);
double probabilityCorrectVolatility = pitCorrectVolatility.pValue (x);
double probabilityTooLowVolatility = pitTooLowVolatility.pValue (x);
System.out.println (
"\t| " +
FormatUtil.FormatDouble (x, 1, 2, 1.) + " | " +
FormatUtil.FormatDouble (probabilityTooHighVolatility - leftProbabilityTooHighVolatility, 1, 8, 1.) + " | " +
FormatUtil.FormatDouble (probabilityCorrectVolatility - leftProbabilityCorrectVolatility, 1, 8, 1.) + " | " +
FormatUtil.FormatDouble (probabilityTooLowVolatility - leftProbabilityTooLowVolatility, 1, 8, 1.) + " ||"
);
leftProbabilityTooHighVolatility = probabilityTooHighVolatility;
leftProbabilityCorrectVolatility = probabilityCorrectVolatility;
leftProbabilityTooLowVolatility = probabilityTooLowVolatility;
}
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int drawCount = 1000000;
double mean = 0.;
double volatilityTooHigh = 3.;
double volatilityCorrect = 2.;
double volatilityTooLow = 1.;
double xLeft = -7.00;
double xRight = 7.00;
double xWidth = 0.50;
Sample sampleVolatilityTooHigh = GenerateSample (
mean,
volatilityTooHigh,
drawCount
);
Sample sampleVolatilityCorrect = GenerateSample (
mean,
volatilityCorrect,
drawCount
);
Sample sampleVolatilityTooLow = GenerateSample (
mean,
volatilityTooLow,
drawCount
);
System.out.println ("\t|-------------------------------------------------||");
System.out.println ("\t| MODEL MTM DISTRIBUTION COMPARISON ||");
System.out.println ("\t|-------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Ordinate ||");
System.out.println ("\t| - p-Value (Volatility Too High) ||");
System.out.println ("\t| - p-Value (Volatility Correct) ||");
System.out.println ("\t| - p-Value (Volatility Too Low) ||");
System.out.println ("\t|-------------------------------------------------||");
ProbabilityPlot (
sampleVolatilityTooHigh.nativeProbabilityIntegralTransform(),
sampleVolatilityCorrect.nativeProbabilityIntegralTransform(),
sampleVolatilityTooLow.nativeProbabilityIntegralTransform(),
xLeft,
xRight,
xWidth
);
System.out.println ("\t|-------------------------------------------------||");
EnvManager.TerminateEnv();
}
}