PykhtinPillarDynamics.java
package org.drip.exposure.regression;
/*
* -*- 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
*
* 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>PykhtinPillarDynamics</i> generates the Dynamics off of the Pillar Vertex Exposure Realizations to be
* used in eventual Exposure Regression using the Pykhtin (2009) Scheme. The References are:
*
* <br><br>
* <ul>
* <li>
* 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 <b>eSSRN</b>
* </li>
* <li>
* 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 <b>eSSRN</b>
* </li>
* <li>
* Albanese, C., and L. Andersen (2014): Accounting for OTC Derivatives: Funding Adjustments and
* the Re-Hypothecation Option https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2482955
* <b>eSSRN</b>
* </li>
* <li>
* Burgard, C., and M. Kjaer (2017): Derivatives Funding, Netting, and Accounting
* https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2534011 <b>eSSRN</b>
* </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/ExposureAnalyticsLibrary.md">Exposure Analytics</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/exposure/README.md">Exposure Group Level Collateralized/Uncollateralized Exposure</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/exposure/regression/README.md">Regression Based Path Exposure Generation</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class PykhtinPillarDynamics
{
private java.util.List<java.lang.Double> _exposureList = null;
/**
* Construct an Instance of PykhtinPillarDynamics from the Exposure Array
*
* @param exposureArray The Exposure Array
*
* @return The VertexRealization Instance
*/
public static final PykhtinPillarDynamics Standard (
final double[] exposureArray)
{
if (null == exposureArray)
{
return null;
}
java.util.List<java.lang.Double> exposureList = new java.util.ArrayList<java.lang.Double>();
int exposureCount = exposureArray.length;
if (0 == exposureCount)
{
return null;
}
for (double exposure : exposureArray)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (exposure))
{
return null;
}
exposureList.add (exposure);
}
java.util.Collections.sort (exposureList);
try
{
return new PykhtinPillarDynamics (exposureList);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
protected PykhtinPillarDynamics (
final java.util.List<java.lang.Double> exposureList)
throws java.lang.Exception
{
if (null == (_exposureList = exposureList) || 0 == _exposureList.size())
{
throw new java.lang.Exception ("PykhtinPillarVertexDynamics Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Exposure Set
*
* @return The Exposure Set
*/
public java.util.List<java.lang.Double> exposureList()
{
return _exposureList;
}
/**
* Retrieve the Pykhtin Pillar Vertex Array
*
* @param localVolatilityGenerationControl The Local Volatility Generation Control
*
* @return The Pykhtin Pillar Vertex Array
*/
public org.drip.exposure.regression.PykhtinPillar[] pillarVertexArray (
final org.drip.exposure.regression.LocalVolatilityGenerationControl localVolatilityGenerationControl)
{
if (null == localVolatilityGenerationControl)
{
return null;
}
int realizationCount = _exposureList.size();
double[] uniformCPDArray = localVolatilityGenerationControl.uniformCPDArray();
int localVolatilityIndexShift = localVolatilityGenerationControl.localVolatilityIndexShift();
double[] impliedBrownianVariateArray = localVolatilityGenerationControl.impliedBrownianVariateArray();
int realizationIndex = 0;
double[] exposureArray = new double[realizationCount];
int localVolatilityIndexFloor = localVolatilityIndexShift;
double[] localVolatilityArray = new double[realizationCount];
int localVolatilityIndexCeiling = realizationCount - localVolatilityIndexShift;
org.drip.exposure.regression.PykhtinPillar[] pillarVertexArray = new
org.drip.exposure.regression.PykhtinPillar[realizationCount];
for (double exposure : _exposureList)
{
exposureArray[realizationIndex++] = exposure;
}
for (int realizationCoordinate = localVolatilityIndexFloor;
realizationCoordinate < localVolatilityIndexCeiling;
++realizationCoordinate)
{
localVolatilityArray[realizationCoordinate] =
(exposureArray[realizationCoordinate - localVolatilityIndexShift] -
exposureArray[realizationCoordinate + localVolatilityIndexShift]) /
(impliedBrownianVariateArray[realizationCoordinate - localVolatilityIndexShift] -
impliedBrownianVariateArray[realizationCoordinate + localVolatilityIndexShift]);
}
for (int realizationCoordinate = 0;
realizationCoordinate < localVolatilityIndexFloor;
++realizationCoordinate)
{
localVolatilityArray[realizationCoordinate] = localVolatilityArray[localVolatilityIndexFloor];
}
for (int realizationCoordinate = localVolatilityIndexCeiling;
realizationCoordinate < realizationCount;
++realizationCoordinate)
{
localVolatilityArray[realizationCoordinate] =
localVolatilityArray[localVolatilityIndexCeiling - 1];
}
for (int realizationCoordinate = 0; realizationCoordinate < realizationCount;
++realizationCoordinate)
{
try
{
pillarVertexArray[realizationCoordinate] =
new org.drip.exposure.regression.PykhtinPillar (
exposureArray[realizationCoordinate],
realizationCoordinate,
uniformCPDArray[realizationCoordinate],
impliedBrownianVariateArray[realizationCoordinate],
localVolatilityArray[realizationCoordinate]
);
++realizationIndex;
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
return pillarVertexArray;
}
/**
* Generate a Local Volatility R^1 To R^1
*
* @param localVolatilityGenerationControl The Local Volatility Generation Control
* @param pillarVertexArray The Array of Pykhtin Pillar Vertexes
*
* @return The Local Volatility R^1 To R^1
*/
public org.drip.function.definition.R1ToR1 localVolatilityR1ToR1 (
final org.drip.exposure.regression.LocalVolatilityGenerationControl localVolatilityGenerationControl,
final org.drip.exposure.regression.PykhtinPillar[] pillarVertexArray)
{
if (null == localVolatilityGenerationControl)
{
return null;
}
int vertexCount = pillarVertexArray.length;
double[] exposureArray = new double[vertexCount];
double[] localVolatilityArray = new double[vertexCount];
for (int vertexIndex = 0; vertexIndex < vertexCount; ++vertexIndex)
{
exposureArray[vertexIndex] = pillarVertexArray[vertexIndex].exposure();
localVolatilityArray[vertexIndex] = pillarVertexArray[vertexIndex].localVolatility();
}
org.drip.spline.stretch.MultiSegmentSequence multiSegmentSequence =
org.drip.spline.stretch.MultiSegmentSequenceBuilder.CreateCalibratedStretchEstimator (
"LocalVolatilityR1ToR1_" + org.drip.numerical.common.StringUtil.GUID(),
exposureArray,
localVolatilityArray,
localVolatilityGenerationControl.segmentCustomBuilderControlArray(),
null,
org.drip.spline.stretch.BoundarySettings.NaturalStandard(),
org.drip.spline.stretch.MultiSegmentSequence.CALIBRATE
);
return null == multiSegmentSequence ? null : multiSegmentSequence.toAU();
}
/**
* Generate a Local Volatility R^1 To R^1
*
* @param localVolatilityGenerationControl The Local Volatility Generation Control
*
* @return The Local Volatility R^1 To R^1
*/
public org.drip.function.definition.R1ToR1 localVolatilityR1ToR1 (
final org.drip.exposure.regression.LocalVolatilityGenerationControl localVolatilityGenerationControl)
{
return localVolatilityR1ToR1 (
localVolatilityGenerationControl,
pillarVertexArray (localVolatilityGenerationControl)
);
}
}