CoordinatedVariationTrajectoryGenerator.java
package org.drip.execution.adaptive;
/*
* -*- 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>CoordinatedVariationTrajectoryGenerator</i> implements the Continuous HJB-based Single Step Optimal
* Cost Trajectory using the 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/adaptive/README.md">Coordinated Variation Based Adaptive Execution</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class CoordinatedVariationTrajectoryGenerator {
/**
* Flag Indicating Trade Rate Initialization from Static Trajectory
*/
public static final int TRADE_RATE_STATIC_INITIALIZATION = 1;
/**
* Flag Indicating Trade Rate Initialization to Zero Initial Value
*/
public static final int TRADE_RATE_ZERO_INITIALIZATION = 2;
private org.drip.execution.strategy.OrderSpecification _os = null;
private int _iTradeRateInitializer = TRADE_RATE_ZERO_INITIALIZATION;
private org.drip.execution.tradingtime.CoordinatedVariation _cv = null;
private org.drip.execution.risk.MeanVarianceObjectiveUtility _mvou = null;
private org.drip.execution.hjb.NonDimensionalCostEvolver _ndce = null;
private org.drip.execution.dynamics.LinearPermanentExpectationParameters realizedLPEP (
final double dblMarketState)
{
try {
return new org.drip.execution.dynamics.LinearPermanentExpectationParameters (new
org.drip.execution.parameters.ArithmeticPriceDynamicsSettings (0., new
org.drip.function.r1tor1.FlatUnivariate (_cv.referenceVolatility() * java.lang.Math.exp
(-0.5 * dblMarketState)), 0.), new
org.drip.execution.profiletime.UniformParticipationRateLinear
(org.drip.execution.impact.ParticipationRateLinear.NoImpact()), new
org.drip.execution.profiletime.UniformParticipationRateLinear
(org.drip.execution.impact.ParticipationRateLinear.SlopeOnly
(_cv.referenceLiquidity() * java.lang.Math.exp
(dblMarketState))));
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* CoordinatedVariationTrajectoryGenerator Constructor
*
* @param os The Order Specification
* @param cv The Coordinated Variation Instance
* @param mvou The Mean Variance Objective Utility Function
* @param ndce The Non Dimensional Cost Evolver
* @param iTradeRateInitializer The Trade Rate Initialization Indicator
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public CoordinatedVariationTrajectoryGenerator (
final org.drip.execution.strategy.OrderSpecification os,
final org.drip.execution.tradingtime.CoordinatedVariation cv,
final org.drip.execution.risk.MeanVarianceObjectiveUtility mvou,
final org.drip.execution.hjb.NonDimensionalCostEvolver ndce,
final int iTradeRateInitializer)
throws java.lang.Exception
{
if (null == (_os = os) || null == (_cv = cv) || null == (_mvou = mvou) || null == (_ndce = ndce) ||
(TRADE_RATE_STATIC_INITIALIZATION != (_iTradeRateInitializer = iTradeRateInitializer) &&
TRADE_RATE_ZERO_INITIALIZATION != _iTradeRateInitializer))
throw new java.lang.Exception
("CoordinatedVariationTrajectoryGenerator Constructor => Invalid Inputs");
}
/**
* Retrieve the Trade Rate Initialization Indicator
*
* @return The Trade Rate Initialization Indicator
*/
public int tradeRateInitializer()
{
return _iTradeRateInitializer;
}
/**
* Retrieve the Order Specification
*
* @return The Order Specification
*/
public org.drip.execution.strategy.OrderSpecification orderSpecification()
{
return _os;
}
/**
* Retrieve the Coordinated Variation Instance
*
* @return The Coordinated Variation Instance
*/
public org.drip.execution.tradingtime.CoordinatedVariation coordinatedVariationConstraint()
{
return _cv;
}
/**
* Retrieve the Non Dimensional Cost Evolver
*
* @return The Non Dimensional Cost Evolver
*/
public org.drip.execution.hjb.NonDimensionalCostEvolver evolver()
{
return _ndce;
}
/**
* Retrieve the Mean Variance Objective Utility Function
*
* @return The Mean Variance Objective Utility Function
*/
public org.drip.execution.risk.MeanVarianceObjectiveUtility objectiveUtility()
{
return _mvou;
}
/**
* Compute The Coordinated Variation Trajectory Determinant Instance
*
* @return The Coordinated Variation Trajectory Determinant Instance
*/
public org.drip.execution.adaptive.CoordinatedVariationTrajectoryDeterminant trajectoryDeterminant()
{
double dblExecutionSize = _os.size();
double dblReferenceLiquidity = _cv.referenceLiquidity();
double dblReferenceVolatility = _cv.referenceVolatility();
double dblRelaxationTime = _ndce.ornsteinUnlenbeckProcess().referenceRelaxationTime();
double dblMeanMarketUrgency = _cv.referenceVolatility() * java.lang.Math.sqrt (_mvou.riskAversion() /
dblReferenceLiquidity);
double dblTradeRateScale = dblExecutionSize / dblRelaxationTime;
try {
return new org.drip.execution.adaptive.CoordinatedVariationTrajectoryDeterminant
(dblExecutionSize, dblRelaxationTime, dblReferenceLiquidity * dblExecutionSize *
dblExecutionSize / dblTradeRateScale, dblTradeRateScale, dblMeanMarketUrgency,
dblMeanMarketUrgency * dblRelaxationTime, dblReferenceLiquidity * dblExecutionSize /
dblReferenceVolatility * java.lang.Math.pow (_os.maxExecutionTime(), -1.5));
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Retrieve the Initial Non Dimensional Cost
*
* @param ms The Initial Market State
* @param dblTradeRateScale The Trade Rate Scale
*
* @return The Initial Non Dimensional Cost
*/
public org.drip.execution.hjb.NonDimensionalCost initializeNonDimensionalCost (
final org.drip.execution.latent.MarketState ms,
final double dblTradeRateScale)
{
if (TRADE_RATE_ZERO_INITIALIZATION == _iTradeRateInitializer)
return org.drip.execution.hjb.NonDimensionalCostSystemic.Zero();
if (null == ms || !org.drip.numerical.common.NumberUtil.IsValid (dblTradeRateScale)) return null;
try {
org.drip.execution.strategy.ContinuousTradingTrajectory ctt =
(org.drip.execution.strategy.ContinuousTradingTrajectory) new
org.drip.execution.nonadaptive.ContinuousAlmgrenChriss (_os,
org.drip.execution.dynamics.ArithmeticPriceEvolutionParametersBuilder.ReferenceCoordinatedVariation
(_cv), _mvou).generate();
if (null == ctt) return null;
double dblNonDimensionalInstantTradeRate = ctt.tradeRate().evaluate (0.) / dblTradeRateScale;
double dblNonDimensionalCostSensitivity = java.lang.Math.exp (ms.liquidity()) *
dblNonDimensionalInstantTradeRate;
return new org.drip.execution.hjb.NonDimensionalCostSystemic (0., dblNonDimensionalCostSensitivity,
dblNonDimensionalCostSensitivity, dblNonDimensionalInstantTradeRate);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Generate the Continuous Coordinated Variation Dynamic Adaptive Trajectory
*
* @param aMS Array of Realized Market States
*
* @return The Continuous Coordinated Variation Dynamic Adaptive Trajectory
*/
public org.drip.execution.adaptive.CoordinatedVariationDynamic adaptive (
final org.drip.execution.latent.MarketState[] aMS)
{
if (null == aMS) return null;
int iNumTimeNode = aMS.length;
if (1 >= iNumTimeNode) return null;
double dblExecutionSize = _os.size();
double dblReferenceLiquidity = _cv.referenceLiquidity();
double dblReferenceVolatility = _cv.referenceVolatility();
double dblRelaxationTime = _ndce.ornsteinUnlenbeckProcess().referenceRelaxationTime();
double dblNonDimensionalTimeIncrement = _os.maxExecutionTime() / (iNumTimeNode - 1) /
dblRelaxationTime;
double dblMeanMarketUrgency = dblReferenceVolatility * java.lang.Math.sqrt (_mvou.riskAversion() /
dblReferenceLiquidity);
org.drip.execution.hjb.NonDimensionalCost[] aNDC = new
org.drip.execution.hjb.NonDimensionalCost[iNumTimeNode];
double[] adblNonDimensionalScaledTradeRate = new double[iNumTimeNode];
double dblTradeRateScale = dblExecutionSize / dblRelaxationTime;
double[] adblNonDimensionalHoldings = new double[iNumTimeNode];
adblNonDimensionalScaledTradeRate[0] = 0.;
adblNonDimensionalHoldings[0] = 1.;
if (null == (aNDC[0] = initializeNonDimensionalCost (aMS[0], dblTradeRateScale))) return null;
for (int i = 1; i < iNumTimeNode; ++i) {
if (null == (aNDC[i] = _ndce.evolve (aNDC[i - 1], aMS[i], dblMeanMarketUrgency *
dblRelaxationTime, (iNumTimeNode - i) * dblNonDimensionalTimeIncrement,
dblNonDimensionalTimeIncrement)))
return null;
adblNonDimensionalScaledTradeRate[i] = adblNonDimensionalHoldings[i - 1] *
aNDC[i].nonDimensionalTradeRate();
adblNonDimensionalHoldings[i] = adblNonDimensionalHoldings[i - 1] -
adblNonDimensionalScaledTradeRate[i] * dblNonDimensionalTimeIncrement;
}
try {
return new org.drip.execution.adaptive.CoordinatedVariationDynamic (new
org.drip.execution.adaptive.CoordinatedVariationTrajectoryDeterminant (dblExecutionSize,
dblRelaxationTime, dblReferenceLiquidity * dblExecutionSize * dblExecutionSize /
dblTradeRateScale, dblTradeRateScale, dblMeanMarketUrgency, dblMeanMarketUrgency *
dblRelaxationTime, dblReferenceLiquidity * dblExecutionSize /
dblReferenceVolatility * java.lang.Math.pow (_os.maxExecutionTime(), -1.5)),
adblNonDimensionalHoldings, adblNonDimensionalScaledTradeRate, aNDC);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Generate a Static, Non-adaptive Trading Trajectory Instance
*
* @return The Static, Non-adaptive Trading Trajectory Instance
*/
public org.drip.execution.adaptive.CoordinatedVariationStatic nonAdaptive()
{
try {
return new org.drip.execution.adaptive.CoordinatedVariationStatic (trajectoryDeterminant(),
(org.drip.execution.optimum.EfficientTradingTrajectoryContinuous) new
org.drip.execution.nonadaptive.ContinuousAlmgrenChriss (_os,
org.drip.execution.dynamics.ArithmeticPriceEvolutionParametersBuilder.ReferenceCoordinatedVariation
(_cv), _mvou).generate());
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Generate the Continuous Coordinated Variation Rolling Horizon Trajectory
*
* @param aMS Array of Realized Market States
*
* @return The Continuous Coordinated Variation Rolling Horizon Trajectory
*/
public org.drip.execution.adaptive.CoordinatedVariationRollingHorizon rollingHorizon (
final org.drip.execution.latent.MarketState[] aMS)
{
if (null == aMS) return null;
int iNumTimeNode = aMS.length;
double[] adblNonDimensionalCost = 0 == iNumTimeNode ? null : new double[iNumTimeNode];
double[] adblNonDimensionalHoldings = 0 == iNumTimeNode ? null : new double[iNumTimeNode];
double[] adblNonDimensionalTradeRate = 0 == iNumTimeNode ? null : new double[iNumTimeNode];
if (0 == iNumTimeNode) return null;
double dblExecutionSize = _os.size();
double dblRiskAversion = _mvou.riskAversion();
double dblExecutionTime = _os.maxExecutionTime();
double dblReferenceLiquidity = _cv.referenceLiquidity();
double dblReferenceVolatility = _cv.referenceVolatility();
double dblRelaxationTime = _ndce.ornsteinUnlenbeckProcess().referenceRelaxationTime();
double dblMeanMarketUrgency = dblReferenceVolatility * java.lang.Math.sqrt (dblRiskAversion /
dblReferenceLiquidity);
double dblNonDimensionalTimeIncrement = dblExecutionTime / (iNumTimeNode - 1) / dblRelaxationTime;
double dblNonDimensionalExecutionTime = dblExecutionTime / dblRelaxationTime;
double dblTradeRateScale = dblExecutionSize / dblRelaxationTime;
adblNonDimensionalTradeRate[iNumTimeNode - 1] = 0.;
adblNonDimensionalHoldings[0] = 1.;
adblNonDimensionalCost[0] = 0.;
for (int i = 0; i < iNumTimeNode - 1; ++i) {
org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep = realizedLPEP
(aMS[i].liquidity());
if (null == lpep) return null;
try {
double dblRealizedVolatility = lpep.arithmeticPriceDynamicsSettings().epochVolatility();
org.drip.execution.strategy.ContinuousTradingTrajectory ctt =
(org.drip.execution.strategy.ContinuousTradingTrajectory) new
org.drip.execution.nonadaptive.ContinuousAlmgrenChriss (new
org.drip.execution.strategy.OrderSpecification (adblNonDimensionalHoldings[i],
dblNonDimensionalExecutionTime - i * dblNonDimensionalTimeIncrement), lpep,
_mvou).generate();
if (null == ctt) return null;
adblNonDimensionalTradeRate[i] = ctt.tradeRate().evaluate (0.);
adblNonDimensionalHoldings[i + 1] = adblNonDimensionalHoldings[i] -
adblNonDimensionalTradeRate[i] * dblNonDimensionalTimeIncrement;
adblNonDimensionalCost[i + 1] = adblNonDimensionalCost[i] + (dblRiskAversion *
dblRealizedVolatility * dblRealizedVolatility * adblNonDimensionalHoldings[i] *
adblNonDimensionalHoldings[i] +
lpep.linearPermanentExpectation().epochLiquidityFunction().slope() *
adblNonDimensionalTradeRate[i] * adblNonDimensionalTradeRate[i]) *
dblNonDimensionalTimeIncrement;
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
}
try {
return new org.drip.execution.adaptive.CoordinatedVariationRollingHorizon (new
org.drip.execution.adaptive.CoordinatedVariationTrajectoryDeterminant (dblExecutionSize,
dblRelaxationTime, dblReferenceLiquidity * dblExecutionSize * dblExecutionSize /
dblTradeRateScale, dblTradeRateScale, dblMeanMarketUrgency, dblMeanMarketUrgency *
dblRelaxationTime, dblReferenceLiquidity * dblExecutionSize /
dblReferenceVolatility * java.lang.Math.pow (_os.maxExecutionTime(), -1.5)),
adblNonDimensionalHoldings, adblNonDimensionalTradeRate,
adblNonDimensionalCost);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}