NonDimensionalCostEvolverSystemic.java
package org.drip.execution.hjb;
/*
* -*- 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
* Copyright (C) 2016 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>NonDimensionalCostEvolverSystemic</i> implements the 1D HJB-based Single Step Optimal Trajectory Cost
* Step Evolver using the Systemic Coordinated Variation Version of the Stochastic Volatility and the
* Transaction Function arising from the Realization of the Market State Variable as described in the
* "Trading Time" Model. The References are:
*
* <br><br>
* <ul>
* <li>
* Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
* Risk</i> <b>3 (2)</b> 5-39
* </li>
* <li>
* Almgren, R. F. (2009): Optimal Trading in a Dynamic Market
* https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
* </li>
* <li>
* Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility <i>SIAM Journal
* of Financial Mathematics</i> <b>3 (1)</b> 163-181
* </li>
* <li>
* Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes <i>Mathematical
* Finance</i> <b>11 (1)</b> 79-96
* </li>
* <li>
* Jones, C. M., G. Kaul, and M. L. Lipson (1994): Transactions, Volume, and Volatility <i>Review of
* Financial Studies</i> <b>7 (4)</b> 631-651
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/README.md">Optimal Impact/Capture Based Trading Trajectories - Deterministic, Stochastic, Static, and Dynamic</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/hjb/README.md">Hamilton Jacobin Bellman Based Optimal Evolution</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class NonDimensionalCostEvolverSystemic extends org.drip.execution.hjb.NonDimensionalCostEvolver
{
/**
* Construct a Standard NonDimensionalCostEvolverSystemic Instance
*
* @param ou The Underlying Ornstein-Unlenbeck Reference Process
*
* @return The Standard NonDimensionalCostEvolverSystemic Instance
*/
public static final NonDimensionalCostEvolverSystemic Standard (
final org.drip.measure.process.OrnsteinUhlenbeck ou)
{
try {
return new NonDimensionalCostEvolverSystemic (ou,
org.drip.execution.hjb.NonDimensionalCostEvolver.SINGULAR_URGENCY_THRESHOLD, true);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
@Override protected double advance (
final org.drip.execution.hjb.NonDimensionalCost ndc,
final org.drip.execution.latent.MarketState ms,
final double[] adblMarketStateTweak,
final double dblNonDimensionalRiskAversion)
throws java.lang.Exception
{
double dblNonDimensionalCost = ndc.realization();
double dblMarketState = ms.liquidity() + adblMarketStateTweak[0];
double dblBurstiness = ornsteinUnlenbeckProcess().referenceBurstiness();
org.drip.execution.hjb.NonDimensionalCostSystemic ndcs =
(org.drip.execution.hjb.NonDimensionalCostSystemic) ndc;
return java.lang.Math.exp (-dblMarketState) * (dblNonDimensionalRiskAversion *
dblNonDimensionalRiskAversion - dblNonDimensionalCost * dblNonDimensionalCost) + 0.5 *
dblBurstiness * dblBurstiness * ndcs.jacobian() - dblMarketState * ndcs.gradient();
}
/**
* NonDimensionalCostEvolverSystemic Constructor
*
* @param ou The Underlying Ornstein-Unlenbeck Reference Process
* @param bAsymptoticEnhancedEulerCorrection Asymptotic Enhanced Euler Correction Application Flag
* @param dblAsymptoticEulerUrgencyThreshold The Asymptotic Euler Urgency Threshold
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public NonDimensionalCostEvolverSystemic (
final org.drip.measure.process.OrnsteinUhlenbeck ou,
final double dblAsymptoticEulerUrgencyThreshold,
final boolean bAsymptoticEnhancedEulerCorrection)
throws java.lang.Exception
{
super (ou, dblAsymptoticEulerUrgencyThreshold, bAsymptoticEnhancedEulerCorrection);
}
@Override public org.drip.execution.hjb.NonDimensionalCost evolve (
final org.drip.execution.hjb.NonDimensionalCost ndc,
final org.drip.execution.latent.MarketState ms,
final double dblNonDimensionalRiskAversion,
final double dblNonDimensionalTime,
final double dblNonDimensionalTimeIncrement)
{
if (null == ndc || !(ndc instanceof org.drip.execution.hjb.NonDimensionalCostSystemic) || null
== ms || !org.drip.numerical.common.NumberUtil.IsValid (dblNonDimensionalRiskAversion) ||
!org.drip.numerical.common.NumberUtil.IsValid (dblNonDimensionalTime) ||
!org.drip.numerical.common.NumberUtil.IsValid (dblNonDimensionalTimeIncrement))
return null;
double dblMarketState = ms.liquidity();
double dblMarketStateIncrement = 0.01 * dblMarketState;
double dblMarketStateExponentiation = java.lang.Math.exp (dblMarketState);
if (asymptoticEulerUrgencyThreshold() * dblNonDimensionalTime < 1.) {
if (!asymptoticEnhancedEulerCorrection())
return org.drip.execution.hjb.NonDimensionalCostSystemic.LinearThreshold
(dblMarketStateExponentiation, dblNonDimensionalTime);
double dblBurstiness = ornsteinUnlenbeckProcess().referenceBurstiness();
double dblNonDimensionalCostCross = -0.5 * dblMarketState * dblMarketStateExponentiation;
return org.drip.execution.hjb.NonDimensionalCostSystemic.EulerEnhancedLinearThreshold
(dblMarketState, ((1. / dblNonDimensionalTimeIncrement) + 0.25 * dblBurstiness *
dblBurstiness) * java.lang.Math.exp (dblMarketState) + dblNonDimensionalCostCross,
dblNonDimensionalCostCross);
}
try {
double dblCostIncrementMid = advance (ndc, ms, new double[] {0.}, dblNonDimensionalRiskAversion)
* dblNonDimensionalTimeIncrement;
double dblCostIncrementUp = advance (ndc, ms, new double[] {dblMarketStateIncrement},
dblNonDimensionalRiskAversion) * dblNonDimensionalTimeIncrement;
double dblCostIncrementDown = advance (ndc, ms, new double[] {-1. * dblMarketStateIncrement},
dblNonDimensionalRiskAversion) * dblNonDimensionalTimeIncrement;
double dblCost = ndc.realization() + dblCostIncrementMid;
return new org.drip.execution.hjb.NonDimensionalCostSystemic (dblCost, 0.5 *
(dblCostIncrementUp - dblCostIncrementDown) / dblMarketStateIncrement, (dblCostIncrementUp +
dblCostIncrementDown - 2. * dblCostIncrementMid) / (dblMarketStateIncrement *
dblMarketStateIncrement), dblCost / dblMarketStateExponentiation);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}