BurgardKjaerBuilder.java
package org.drip.xva.vertex;
/*
* -*- 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
* Copyright (C) 2017 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>BurgardKjaerBuilder</i> contains the Builders that construct the Burgard Kjaer Vertex using a Variant
* of the Generalized Burgard Kjaer (2013) Scheme. The References are:
*
* <br><br>
* <ul>
* <li>
* Burgard, C., and M. Kjaer (2014): PDE Representations of Derivatives with Bilateral Counter-party
* Risk and Funding Costs <i>Journal of Credit Risk</i> <b>7 (3)</b> 1-19
* </li>
* <li>
* Burgard, C., and M. Kjaer (2014): In the Balance <i>Risk</i> <b>24 (11)</b> 72-75
* </li>
* <li>
* Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk <i>Risk</i> <b>20 (2)</b>
* 86-90
* </li>
* <li>
* Li, B., and Y. Tang (2007): <i>Quantitative Analysis, Derivatives Modeling, and Trading
* Strategies in the Presence of Counter-party Credit Risk for the Fixed Income Market</i>
* <b>World Scientific Publishing</b> Singapore
* </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/XVAAnalyticsLibrary.md">XVA Analytics Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/xva/README.md">Valuation Adjustments that account for Collateral, CC Credit/Debt and Funding Overhead</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/xva/vertex/README.md">XVA Hypothecation Group Vertex Generators</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class BurgardKjaerBuilder
{
/**
* Construct the Initial Dynamic Dealer Portfolio
*
* @param anchorDate The Anchor Date
* @param forward The Unrealized Forward Exposure
* @param marketVertex The Market Vertex
* @param closeOutScheme The Generic Close Out Instance
*
* @return The Burgard Kjaer Dealer Portfolio Vertex
*/
public static final org.drip.xva.vertex.BurgardKjaer Initial (
final org.drip.analytics.date.JulianDate anchorDate,
final double forward,
final org.drip.exposure.universe.MarketVertex marketVertex,
final org.drip.xva.definition.CloseOut closeOutScheme)
{
if (null == marketVertex)
{
return null;
}
org.drip.xva.hypothecation.CollateralGroupVertexCloseOut collateralGroupVertexCloseOut =
org.drip.xva.hypothecation.CollateralGroupVertexCloseOut.Standard (
closeOutScheme,
forward,
0.
);
org.drip.xva.vertex.BurgardKjaerExposure burgardKjaerVertexExposure =
org.drip.xva.vertex.BurgardKjaerExposure.Initial (
forward,
collateralGroupVertexCloseOut
);
if (null == burgardKjaerVertexExposure)
{
return null;
}
double fundingExposure = burgardKjaerVertexExposure.funding();
double dealerDefaultCloseOut = collateralGroupVertexCloseOut.dealer();
org.drip.exposure.universe.MarketVertexEntity dealerMarketVertex = marketVertex.dealer();
double dealerSubordinateFundingMarketVertex = dealerMarketVertex.subordinateFundingReplicator();
double dealerSurvival = dealerMarketVertex.survivalProbability();
double dealerSeniorRecoveryRate = dealerMarketVertex.seniorRecoveryRate();
double dealerSubordinateRecoveryRate = dealerMarketVertex.subordinateRecoveryRate();
double clientSurvival = marketVertex.client().survivalProbability();
double incrementalDealerSurvival = dealerSurvival - 1.;
double adjustedExposure =
forward + dealerSurvival * (clientSurvival - 1.) * burgardKjaerVertexExposure.credit() +
clientSurvival * incrementalDealerSurvival * burgardKjaerVertexExposure.debt() +
clientSurvival * incrementalDealerSurvival * fundingExposure -
dealerSurvival * clientSurvival * marketVertex.csaSpread() *
burgardKjaerVertexExposure.variationMarginPosting();
try
{
return new org.drip.xva.vertex.BurgardKjaer (
anchorDate,
forward,
0.,
burgardKjaerVertexExposure,
collateralGroupVertexCloseOut,
new org.drip.xva.derivative.ReplicationPortfolioVertexDealer (
(fundingExposure + dealerSubordinateRecoveryRate * adjustedExposure - dealerDefaultCloseOut) /
(dealerSeniorRecoveryRate - dealerSubordinateRecoveryRate) / dealerMarketVertex.seniorFundingReplicator(),
(fundingExposure + dealerSeniorRecoveryRate * adjustedExposure - dealerDefaultCloseOut) /
(dealerSubordinateRecoveryRate - dealerSeniorRecoveryRate) / dealerSubordinateFundingMarketVertex
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct a Path-wise Dynamic Dealer Portfolio
*
* @param anchorDate The Anchor Date
* @param collateralGroupVertexExposure The Raw Collateral Group Vertex Exposure
* @param marketEdge The Market Edge
* @param collateralGroupVertexCloseOut The Collateral Group Vertex Close Out
* @param burgardKjaerVertexExposure The Collateral Group Vertex Exposure Decomposition
*
* @return The Burgard Kjaer Dealer Portfolio Vertex
*/
public static final org.drip.xva.vertex.BurgardKjaer DealerPortfolioBuilder (
final org.drip.analytics.date.JulianDate anchorDate,
final org.drip.xva.hypothecation.CollateralGroupVertexExposure collateralGroupVertexExposure,
final org.drip.exposure.universe.MarketEdge marketEdge,
final org.drip.xva.hypothecation.CollateralGroupVertexCloseOut collateralGroupVertexCloseOut,
final org.drip.xva.vertex.BurgardKjaerExposure burgardKjaerVertexExposure)
{
if (null == collateralGroupVertexExposure ||
null == marketEdge ||
null == collateralGroupVertexCloseOut ||
null == burgardKjaerVertexExposure)
{
return null;
}
double fundingExposure = burgardKjaerVertexExposure.funding();
double dealerDefaultCloseOut = collateralGroupVertexCloseOut.dealer();
org.drip.exposure.universe.MarketVertex marketVertexStart = marketEdge.start();
org.drip.exposure.universe.MarketVertex marketVertexFinish = marketEdge.finish();
org.drip.exposure.universe.MarketVertexEntity dealerMarketVertexFinish = marketVertexFinish.dealer();
double dealerSubordinateFundingMarketVertexFinish = dealerMarketVertexFinish.subordinateFundingReplicator();
double dealerSurvivalFinish = dealerMarketVertexFinish.survivalProbability();
double dealerSeniorRecoveryRateFinish = dealerMarketVertexFinish.seniorRecoveryRate();
double dealerSubordinateRecoveryRateFinish = dealerMarketVertexFinish.subordinateRecoveryRate();
double clientSurvivalFinish = marketVertexFinish.client().survivalProbability();
double incrementalDealerSurvival = dealerSurvivalFinish -
(null == marketVertexStart ? 1. : marketVertexStart.dealer().survivalProbability());
double adjustedExposure =
collateralGroupVertexExposure.uncollateralized() +
dealerSurvivalFinish *
(clientSurvivalFinish -
(null == marketVertexStart ? 1. : marketVertexStart.client().survivalProbability())) *
burgardKjaerVertexExposure.credit() +
clientSurvivalFinish * incrementalDealerSurvival * burgardKjaerVertexExposure.debt() +
clientSurvivalFinish * incrementalDealerSurvival * fundingExposure -
dealerSurvivalFinish * clientSurvivalFinish * marketVertexFinish.csaSpread() *
burgardKjaerVertexExposure.variationMarginPosting();
try
{
return new org.drip.xva.vertex.BurgardKjaer (
anchorDate,
collateralGroupVertexExposure.variationMarginEstimate(),
collateralGroupVertexExposure.tradePayment(),
burgardKjaerVertexExposure,
collateralGroupVertexCloseOut,
new org.drip.xva.derivative.ReplicationPortfolioVertexDealer (
(fundingExposure + dealerSubordinateRecoveryRateFinish * adjustedExposure -
dealerDefaultCloseOut) / (dealerSeniorRecoveryRateFinish -
dealerSubordinateRecoveryRateFinish) /
dealerMarketVertexFinish.seniorFundingReplicator(),
(fundingExposure + dealerSeniorRecoveryRateFinish * adjustedExposure - dealerDefaultCloseOut)
/ (dealerSubordinateRecoveryRateFinish - dealerSeniorRecoveryRateFinish) /
dealerSubordinateFundingMarketVertexFinish
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct a Standard Instance of BurgardKjaerVertex using the specified Hedge Error with Two Dealer
* Bonds
*
* @param anchorDate The Vertex Date Anchor
* @param exposure The Exposure at the Path Vertex Time Node
* @param realizedCashFlow The Default Window Realized Cash-flow at the Path Vertex Time Node
* @param collateralBalance The Collateral Balance at the Path Vertex Time Node
* @param hedgeError The Hedge Error
* @param marketEdge The Market Edge
* @param closeOutScheme The Generic Close-Out Evaluator Instance
*
* @return The Standard Instance of BurgardKjaerVertex using the specified Hedge Error with Two Dealer
* Bonds
*/
public static final org.drip.xva.vertex.BurgardKjaer HedgeErrorDualBond (
final org.drip.analytics.date.JulianDate anchorDate,
final double exposure,
final double realizedCashFlow,
final double collateralBalance,
final double hedgeError,
final org.drip.exposure.universe.MarketEdge marketEdge,
final org.drip.xva.definition.CloseOut closeOutScheme)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (exposure) ||
!org.drip.numerical.common.NumberUtil.IsValid (realizedCashFlow) ||
!org.drip.numerical.common.NumberUtil.IsValid (collateralBalance) ||
!org.drip.numerical.common.NumberUtil.IsValid (hedgeError))
{
return null;
}
double uncollateralizedExposure = exposure + realizedCashFlow;
double collateralizedExposure = uncollateralizedExposure - collateralBalance;
org.drip.xva.hypothecation.CollateralGroupVertexCloseOut collateralGroupVertexCloseOut =
org.drip.xva.hypothecation.CollateralGroupVertexCloseOut.Standard (
closeOutScheme,
uncollateralizedExposure,
collateralBalance
);
if (null == collateralGroupVertexCloseOut)
{
return null;
}
try
{
return DealerPortfolioBuilder (
anchorDate,
new org.drip.xva.hypothecation.CollateralGroupVertexExposure (
exposure,
realizedCashFlow
),
marketEdge,
collateralGroupVertexCloseOut,
new org.drip.xva.vertex.BurgardKjaerExposure (
collateralizedExposure - collateralGroupVertexCloseOut.client(),
collateralizedExposure - collateralGroupVertexCloseOut.dealer(),
hedgeError,
collateralBalance
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct a Standard Instance of BurgardKjaerVertex using semi-replication with no Short-fall at own
* Default using Two Bonds
*
* @param anchorDate The Vertex Date Anchor
* @param exposure The Exposure at the Path Vertex Time Node
* @param realizedCashFlow The Default Window Realized Cash-flow at the Path Vertex Time Node
* @param collateralBalance The Collateral Balance at the Path Vertex Time Node
* @param marketEdge The Market Edge
* @param closeOutScheme The Generic Close-Out Evaluator Instance
*
* @return The Standard Instance of BurgardKjaerVertex using semi-replication with no Short-fall at own
* Default using Two Bonds
*/
public static final org.drip.xva.vertex.BurgardKjaer SemiReplicationDualBond (
final org.drip.analytics.date.JulianDate anchorDate,
final double exposure,
final double realizedCashFlow,
final double collateralBalance,
final org.drip.exposure.universe.MarketEdge marketEdge,
final org.drip.xva.definition.CloseOut closeOutScheme)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (exposure) ||
!org.drip.numerical.common.NumberUtil.IsValid (realizedCashFlow) ||
!org.drip.numerical.common.NumberUtil.IsValid (collateralBalance))
{
return null;
}
double uncollateralizedExposure = exposure + realizedCashFlow;
double collateralizedExposure = uncollateralizedExposure - collateralBalance;
try
{
return DealerPortfolioBuilder (
anchorDate,
new org.drip.xva.hypothecation.CollateralGroupVertexExposure (
exposure,
realizedCashFlow
),
marketEdge,
org.drip.xva.hypothecation.CollateralGroupVertexCloseOut.Standard (
closeOutScheme,
uncollateralizedExposure,
collateralBalance
),
new org.drip.xva.vertex.BurgardKjaerExposure (
0. < collateralizedExposure ? collateralizedExposure : 0.,
0. > collateralizedExposure ? collateralizedExposure : 0.,
0. < collateralizedExposure ? collateralizedExposure : 0.,
collateralBalance
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct a Standard Instance of BurgardKjaerVertex using a Fully Collateralized Strategy, i.e., also
* referred to as the 2 Way Gold Plated CSA
*
* @param anchorDate The Vertex Date Anchor
* @param exposure The Exposure at the Path Vertex Time Node
* @param realizedCashFlow The Default Window Realized Cash-flow at the Path Vertex Time Node
* @param marketEdge The Market Edge
* @param closeOutScheme The Generic Close-Out Evaluator Instance
*
* @return The Standard Instance of BurgardKjaerVertex using using a Fully Collateralized Strategy
*/
public static final org.drip.xva.vertex.BurgardKjaer GoldPlatedTwoWayCSA (
final org.drip.analytics.date.JulianDate anchorDate,
final double exposure,
final double realizedCashFlow,
final org.drip.exposure.universe.MarketEdge marketEdge,
final org.drip.xva.definition.CloseOut closeOutScheme)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (exposure) ||
!org.drip.numerical.common.NumberUtil.IsValid (realizedCashFlow))
{
return null;
}
double uncollateralizedExposure = exposure + realizedCashFlow;
try
{
return DealerPortfolioBuilder (
anchorDate,
new org.drip.xva.hypothecation.CollateralGroupVertexExposure (
exposure,
realizedCashFlow
),
marketEdge,
org.drip.xva.hypothecation.CollateralGroupVertexCloseOut.Standard (
closeOutScheme,
uncollateralizedExposure,
uncollateralizedExposure
),
new org.drip.xva.vertex.BurgardKjaerExposure (
0.,
0.,
0.,
uncollateralizedExposure
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct a Standard Instance of BurgardKjaerVertex using One Way CSA
*
* @param anchorDate The Vertex Date Anchor
* @param exposure The Exposure at the Path Vertex Time Node
* @param realizedCashFlow The Default Window Realized Cash-flow at the Path Vertex Time Node
* @param marketEdge The Market Edge
* @param closeOutScheme The Generic Close-Out Evaluator Instance
*
* @return The Standard Instance of BurgardKjaerVertex using One Way CSA
*/
public static final org.drip.xva.vertex.BurgardKjaer OneWayCSA (
final org.drip.analytics.date.JulianDate anchorDate,
final double exposure,
final double realizedCashFlow,
final org.drip.exposure.universe.MarketEdge marketEdge,
final org.drip.xva.definition.CloseOut closeOutScheme)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (exposure) ||
!org.drip.numerical.common.NumberUtil.IsValid (realizedCashFlow))
{
return null;
}
double uncollateralizedExposure = exposure + realizedCashFlow;
double collateralBalance = 0. > uncollateralizedExposure ? uncollateralizedExposure : 0.;
try
{
return DealerPortfolioBuilder (
anchorDate,
new org.drip.xva.hypothecation.CollateralGroupVertexExposure (
exposure,
realizedCashFlow
),
marketEdge,
org.drip.xva.hypothecation.CollateralGroupVertexCloseOut.Standard (
closeOutScheme,
uncollateralizedExposure,
collateralBalance
),
new org.drip.xva.vertex.BurgardKjaerExposure (
0. < uncollateralizedExposure ? uncollateralizedExposure : 0.,
0.,
0. < uncollateralizedExposure ? uncollateralizedExposure : 0.,
collateralBalance
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct a Standard Instance of BurgardKjaerVertex using the "Set Off" Legal Agreement Scheme
*
* @param anchorDate The Vertex Date Anchor
* @param exposure The Exposure at the Path Vertex Time Node
* @param realizedCashFlow The Default Window Realized Cash-flow at the Path Vertex Time Node
* @param collateralBalance The Collateral Balance at the Path Vertex Time Node
* @param marketEdge The Market Edge
*
* @return The Standard Instance of BurgardKjaerVertex using the "Set Off" Legal Agreement Scheme
*/
public static final org.drip.xva.vertex.BurgardKjaer SetOff (
final org.drip.analytics.date.JulianDate anchorDate,
final double exposure,
final double realizedCashFlow,
final double collateralBalance,
final org.drip.exposure.universe.MarketEdge marketEdge)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (exposure) ||
!org.drip.numerical.common.NumberUtil.IsValid (realizedCashFlow) ||
!org.drip.numerical.common.NumberUtil.IsValid (collateralBalance))
{
return null;
}
org.drip.exposure.universe.MarketVertex marketVertexFinish = marketEdge.finish();
double dealerSeniorRecoveryRateFinish = marketVertexFinish.dealer().seniorRecoveryRate();
double clientRecoveryFinish = marketVertexFinish.client().seniorRecoveryRate();
double collateralizedExposure = exposure + realizedCashFlow - collateralBalance;
try
{
return DealerPortfolioBuilder (
anchorDate,
new org.drip.xva.hypothecation.CollateralGroupVertexExposure (
exposure,
realizedCashFlow
),
marketEdge,
new org.drip.xva.hypothecation.CollateralGroupVertexCloseOut (
collateralizedExposure * dealerSeniorRecoveryRateFinish,
collateralizedExposure * clientRecoveryFinish
),
new org.drip.xva.vertex.BurgardKjaerExposure (
collateralizedExposure * (1. - clientRecoveryFinish),
collateralizedExposure * (1. - dealerSeniorRecoveryRateFinish),
0.,
collateralBalance
)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}