LocalVolatilityGenerationControl.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>LocalVolatilityGenerationControl</i> holds the Parameters the control the Calculation of the Local
* Volatility in the Pykhtin (2009) Brownian Bridge Calibration. 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 LocalVolatilityGenerationControl
{
/**
* The Pyhktin (2009) Empirical Floor
*/
public static final int PYKHTIN_2009_EMPIRICAL_FLOOR = 20;
/**
* The Pyhktin (2009) Empirical Ceiling Factor
*/
public static final double PYKHTIN_2009_EMPIRICAL_CEILING_FACTOR = 0.05;
/**
* The Local Volatility Smooth Floor Bias
*/
public static final double LOCAL_VOLATILITY_SMOOTHING_FLOOR_BIAS = 0.90;
private double[] _uniformCPDArray = null;
private int _localVolatilityIndexShift = -1;
private double[] _impliedBrownianVariateArray = null;
private org.drip.spline.params.SegmentCustomBuilderControl[] _segmentCustomBuilderControlArray = null;
/**
* Construct a Standard Instance of LocalVolatilityGenerationControl
*
* @param ensembleSize Size of the Distribution Ensemble
*
* @return Standard Instance of LocalVolatilityGenerationControl
*/
public static final LocalVolatilityGenerationControl Standard (
final int ensembleSize)
{
if (PYKHTIN_2009_EMPIRICAL_FLOOR > ensembleSize)
{
return null;
}
double[] uniformCPDArray = new double[ensembleSize];
double[] impliedBrownianVariateArray = new double[ensembleSize];
int localVolatilityIndexShift = (int) (LOCAL_VOLATILITY_SMOOTHING_FLOOR_BIAS *
PYKHTIN_2009_EMPIRICAL_FLOOR + (1 - LOCAL_VOLATILITY_SMOOTHING_FLOOR_BIAS) * ensembleSize);
if (PYKHTIN_2009_EMPIRICAL_FLOOR > localVolatilityIndexShift)
{
return null;
}
for (int realizationCoordinate = 0;
realizationCoordinate < ensembleSize;
++realizationCoordinate)
{
try
{
impliedBrownianVariateArray[realizationCoordinate] =
org.drip.measure.gaussian.NormalQuadrature.InverseCDF
(uniformCPDArray[realizationCoordinate] = (((double) realizationCoordinate) + 0.5) /
((double) ensembleSize));
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
try
{
org.drip.spline.params.SegmentCustomBuilderControl[] segmentCustomBuilderControlArray = new
org.drip.spline.params.SegmentCustomBuilderControl[ensembleSize - 1];
org.drip.spline.params.SegmentCustomBuilderControl segmentCustomBuilderControl = new
org.drip.spline.params.SegmentCustomBuilderControl (
org.drip.spline.stretch.MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
new org.drip.spline.basis.PolynomialFunctionSetParams (2),
org.drip.spline.params.SegmentInelasticDesignControl.Create (
0,
2
),
new org.drip.spline.params.ResponseScalingShapeControl (
true,
new org.drip.function.r1tor1.QuadraticRationalShapeControl (0.)
),
null
);
for (int realizationCoordinate = 0;
realizationCoordinate < ensembleSize - 1;
++realizationCoordinate)
{
segmentCustomBuilderControlArray[realizationCoordinate] = segmentCustomBuilderControl;
}
return new LocalVolatilityGenerationControl (
localVolatilityIndexShift,
uniformCPDArray,
impliedBrownianVariateArray,
segmentCustomBuilderControlArray
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* LocalVolatilityGenerationControl Constructor
*
* @param localVolatilityIndexShift The Local Volatility Index Shift
* @param uniformCPDArray The Uniform Cumulative Probability Density Array
* @param impliedBrownianVariateArray The Implied Brownian Variate Array
* @param segmentCustomBuilderControlArray Array of Segment Builder Control
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public LocalVolatilityGenerationControl (
final int localVolatilityIndexShift,
final double[] uniformCPDArray,
final double[] impliedBrownianVariateArray,
final org.drip.spline.params.SegmentCustomBuilderControl[] segmentCustomBuilderControlArray)
throws java.lang.Exception
{
if (0 >= (_localVolatilityIndexShift = localVolatilityIndexShift) ||
null == (_uniformCPDArray = uniformCPDArray) ||
null == (_impliedBrownianVariateArray = impliedBrownianVariateArray) ||
null == (_segmentCustomBuilderControlArray = segmentCustomBuilderControlArray))
{
throw new java.lang.Exception ("LocalVolatilityGenerationControl Constructor => Invalid Inputs");
}
int uniformCPDArraySize = _uniformCPDArray.length;
if (0 == uniformCPDArraySize ||
uniformCPDArraySize != _impliedBrownianVariateArray.length ||
uniformCPDArraySize != _segmentCustomBuilderControlArray.length + 1)
{
throw new java.lang.Exception ("LocalVolatilityGenerationControl Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Local Volatility Index Shift
*
* @return The Local Volatility Index Shift
*/
public int localVolatilityIndexShift()
{
return _localVolatilityIndexShift;
}
/**
* Retrieve the Uniform Cumulative Probability Density Array
*
* @return The Uniform Cumulative Probability Density Array
*/
public double[] uniformCPDArray()
{
return _uniformCPDArray;
}
/**
* Retrieve the Implied Brownian Variate Array
*
* @return The Implied Brownian Variate Array
*/
public double[] impliedBrownianVariateArray()
{
return _impliedBrownianVariateArray;
}
/**
* Retrieve the Custom Segment Builder Control Array
*
* @return The Custom Segment Builder Control Array
*/
public org.drip.spline.params.SegmentCustomBuilderControl[] segmentCustomBuilderControlArray()
{
return _segmentCustomBuilderControlArray;
}
}