ContinuousCoordinatedVariationStochastic.java
package org.drip.execution.nonadaptive;
/*
* -*- 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>ContinuousCoordinatedVariationStochastic</i> uses the Coordinated Variation Version of the Linear
* Participation Rate Transaction Function as described in the "Trading Time" Model to construct an Optimal
* Trading Trajectory in the T To Infinite Limit. 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/nonadaptive/README.md">Almgren-Chriss Static Optimal Trajectory</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ContinuousCoordinatedVariationStochastic extends
org.drip.execution.nonadaptive.StaticOptimalSchemeContinuous {
/**
* Create the Standard ContinuousCoordinatedVariationStochastic Instance
*
* @param dblStartHoldings Trajectory Start Holdings
* @param dblFinishTime Trajectory Finish Time
* @param apep The Arithmetic Price Evolution Parameters
* @param dblRiskAversion The Risk Aversion Parameter
*
* @return The ContinuousCoordinatedVariationStochastic Instance
*/
public static final ContinuousCoordinatedVariationStochastic Standard (
final double dblStartHoldings,
final double dblFinishTime,
final org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep,
final double dblRiskAversion)
{
try {
return new ContinuousCoordinatedVariationStochastic (new
org.drip.execution.strategy.OrderSpecification (dblStartHoldings, dblFinishTime), apep, new
org.drip.execution.risk.MeanVarianceObjectiveUtility (dblRiskAversion));
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
private ContinuousCoordinatedVariationStochastic (
final org.drip.execution.strategy.OrderSpecification os,
final org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep,
final org.drip.execution.risk.MeanVarianceObjectiveUtility mvou)
throws java.lang.Exception
{
super (os, apep, mvou);
}
@Override public org.drip.execution.optimum.EfficientTradingTrajectory generate()
{
org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep =
(org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters) priceEvolutionParameters();
org.drip.execution.profiletime.BackgroundParticipationRate bprTemporary =
apep.temporaryExpectation();
if (!(bprTemporary instanceof org.drip.execution.profiletime.BackgroundParticipationRateLinear))
return null;
double dblInitialVolatility = java.lang.Double.NaN;
final org.drip.execution.profiletime.BackgroundParticipationRateLinear bprlTemporary =
(org.drip.execution.profiletime.BackgroundParticipationRateLinear) bprTemporary;
org.drip.execution.impact.TransactionFunctionLinear tflTemporaryExpectation =
bprlTemporary.epochLiquidityFunction();
try {
dblInitialVolatility = apep.arithmeticPriceDynamicsSettings().epochVolatility();
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
final double dblEpochVolatility = dblInitialVolatility;
final double dblEpochLiquidity = tflTemporaryExpectation.slope();
final double dblLambda = ((org.drip.execution.risk.MeanVarianceObjectiveUtility)
objectiveUtility()).riskAversion();
double dblEpochUrgency = java.lang.Math.sqrt (dblLambda * dblEpochVolatility * dblEpochVolatility /
dblEpochLiquidity);
final org.drip.function.definition.R1ToR1 r1ToR1VolatilityFunction =
apep.arithmeticPriceDynamicsSettings().volatilityFunction();
org.drip.execution.strategy.OrderSpecification os = orderSpecification();
final double dblT = os.maxExecutionTime();
final double dblX = os.size();
final org.drip.function.definition.R1ToR1 r1ToR1Holdings = new org.drip.function.definition.R1ToR1
(null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
double dblVolatility = r1ToR1VolatilityFunction.evaluate (dblTime);
double dblKappa = java.lang.Math.sqrt (dblLambda * dblVolatility * dblVolatility /
bprlTemporary.liquidityFunction (dblTime).slope());
return java.lang.Math.sinh (dblKappa * (dblT - dblTime)) / java.lang.Math.sinh (dblKappa *
dblT) * dblX;
}
};
org.drip.function.definition.R1ToR1 r1ToR1TradeRate = new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
double dblVolatility = r1ToR1VolatilityFunction.evaluate (dblTime);
return java.lang.Math.sqrt (dblLambda * dblVolatility * dblVolatility /
bprlTemporary.liquidityFunction (dblTime).slope()) * r1ToR1Holdings.evaluate (dblTime);
}
};
final org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectationRate = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
double dblHoldings = r1ToR1Holdings.evaluate (dblTime);
double dblVolatility = r1ToR1VolatilityFunction.evaluate (dblTime);
return java.lang.Math.sqrt (dblLambda * dblVolatility * dblVolatility *
bprlTemporary.liquidityFunction (dblTime).slope()) * dblHoldings * dblHoldings;
}
};
org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectation = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
return r1ToR1TransactionCostExpectationRate.integrate (dblTime, dblT);
}
};
final org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVarianceRate = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
double dblHoldings = r1ToR1Holdings.evaluate (dblTime);
double dblVolatility = r1ToR1VolatilityFunction.evaluate (dblTime);
return dblVolatility * dblVolatility * dblHoldings * dblHoldings;
}
};
org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVariance = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
return r1ToR1TransactionCostVarianceRate.integrate (dblTime, dblT);
}
};
try {
return new org.drip.execution.optimum.EfficientTradingTrajectoryContinuous (dblT,
dblEpochLiquidity * dblEpochUrgency * dblX * dblX / java.lang.Math.tanh (dblEpochUrgency *
dblT), r1ToR1TransactionCostExpectation.evaluate (0.), 1. / dblEpochUrgency,
dblEpochLiquidity * dblX / (dblT * dblEpochVolatility * java.lang.Math.sqrt (dblT)),
r1ToR1Holdings, r1ToR1TradeRate, r1ToR1TransactionCostExpectation,
r1ToR1TransactionCostVariance);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}