PykhtinBrownianBridgeSegment.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>PykhtinBrownianBridgeSegment</i> generates the Segment Regression Based Exposures off of the
* corresponding Pillar Vertexes 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 PykhtinBrownianBridgeSegment
{
private org.drip.exposure.regression.PillarVertex _leftPillar = null;
private org.drip.exposure.regression.PillarVertex _rightPillar = null;
private org.drip.function.definition.R1ToR1 _rightPillarLocalVolatility = null;
/**
* PykhtinBrownianBridgeSegment Constructor
*
* @param leftPillar The Left Pillar Vertex
* @param rightPillar The Right Pillar Vertex
* @param rightPillarLocalVolatility The Right Pillar Local Volatility
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public PykhtinBrownianBridgeSegment (
final org.drip.exposure.regression.PillarVertex leftPillar,
final org.drip.exposure.regression.PillarVertex rightPillar,
final org.drip.function.definition.R1ToR1 rightPillarLocalVolatility)
throws java.lang.Exception
{
if (null == (_leftPillar = leftPillar) ||
null == (_rightPillar = rightPillar) ||
_leftPillar.date() >= _rightPillar.date() ||
null == (_rightPillarLocalVolatility = rightPillarLocalVolatility))
{
throw new java.lang.Exception ("PykhtinBrownianBridgeSegment Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Left Pillar Vertex
*
* @return The Left Pillar Vertex
*/
public org.drip.exposure.regression.PillarVertex leftPillar()
{
return _leftPillar;
}
/**
* Retrieve the Right Pillar Vertex
*
* @return The Right Pillar Vertex
*/
public org.drip.exposure.regression.PillarVertex rightPillar()
{
return _rightPillar;
}
/**
* Retrieve the Right Pillar Local Volatility
*
* @return The Right Pillar Local Volatility
*/
public org.drip.function.definition.R1ToR1 rightPillarLocalVolatility()
{
return _rightPillarLocalVolatility;
}
/**
* Generate the Dense (Complete) Segment Exposures
*
* @param denseExposureTrajectory The Dense Exposure Trajectory
* @param wanderTrajectory The Wander Date Trajectory
*
* @return The Dense (Complete) Segment Exposures
*/
public boolean denseExposureTrajectoryUpdate (
final java.util.Map<java.lang.Integer, java.lang.Double> denseExposureTrajectory,
final java.util.Map<java.lang.Integer, java.lang.Double> wanderTrajectory)
{
if (null == denseExposureTrajectory || null == wanderTrajectory)
{
return false;
}
int leftPillarDate = _leftPillar.date();
int rightPillarDate = _rightPillar.date();
double leftPillarExposure = _leftPillar.exposure();
double rightPillarExposure = _rightPillar.exposure();
int dateWidth = rightPillarDate - leftPillarDate;
double urgency = 1. / dateWidth;
double localVolatility = java.lang.Double.NaN;
double localDrift = (rightPillarExposure - leftPillarExposure) * urgency;
denseExposureTrajectory.put (
leftPillarDate,
leftPillarExposure
);
denseExposureTrajectory.put (
rightPillarDate,
rightPillarExposure
);
try
{
localVolatility = _rightPillarLocalVolatility.evaluate (rightPillarExposure);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return false;
}
for (int dateIndex = dateWidth - 1; dateIndex > 0; --dateIndex)
{
int date = leftPillarDate + dateIndex;
if (!wanderTrajectory.containsKey (date))
{
return false;
}
denseExposureTrajectory.put (
date,
rightPillarExposure - localDrift * (dateWidth - dateIndex) + localVolatility * urgency *
wanderTrajectory.get (date) * java.lang.Math.sqrt (dateIndex * (dateWidth - dateIndex))
);
}
return true;
}
}