LinearImpactTrajectoryEstimator.java

package org.drip.execution.capture;

/*
 * -*- 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>LinearImpactTrajectoryEstimator</i> estimates the Price/Cost Distribution associated with the Trading
 * Trajectory generated using the Linear Market Impact Evolution Parameters. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
 *      </li>
 *      <li>
 *          Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
 *              Risk</i> <b>3 (2)</b> 5-39
 *      </li>
 *      <li>
 *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
 *              Markets</i> <b>1</b> 1-50
 *      </li>
 *      <li>
 *          Chan, L. K. C., and J. Lakonishak (1995): The Behavior of Stock Prices around Institutional
 *              Trades <i>Journal of Finance</i> <b>50</b> 1147-1174
 *      </li>
 *      <li>
 *          Keim, D. B., and A. Madhavan (1997): Transaction Costs and Investment Style: An Inter-exchange
 *              Analysis of Institutional Equity Trades <i>Journal of Financial Economics</i> <b>46</b>
 *              265-292
 *      </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/capture/README.md">Execution Trajectory Transaction Cost Capture</a></li>
 *  </ul>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class LinearImpactTrajectoryEstimator extends org.drip.execution.capture.TrajectoryShortfallEstimator
{

    /**
     * LinearImpactTrajectoryEstimator Constructor
     * 
     * @param tt The Trading Trajectory Instance
     *  
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public LinearImpactTrajectoryEstimator (
        final org.drip.execution.strategy.DiscreteTradingTrajectory tt)
        throws java.lang.Exception
    {
        super (tt);
    }

    @Override public org.drip.measure.gaussian.R1UnivariateNormal totalCostDistributionSynopsis (
        final org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep)
    {
        if (null == apep) return null;

        double dblMarketCoreVolatility = java.lang.Double.NaN;
        org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep =
            (org.drip.execution.dynamics.LinearPermanentExpectationParameters) apep;

        double dblPermanentLinearImpactParameter = ((org.drip.execution.impact.TransactionFunctionLinear)
            lpep.linearPermanentExpectation().epochImpactFunction()).slope();

        org.drip.execution.impact.TransactionFunctionLinear tflTemporaryExpectation =
            (org.drip.execution.impact.TransactionFunctionLinear)
                apep.temporaryExpectation().epochImpactFunction();

        double dblTemporaryLinearImpactParameter = tflTemporaryExpectation.slope();

        double dblTemporaryOffsetImpactParameter = tflTemporaryExpectation.offset();

        org.drip.execution.strategy.DiscreteTradingTrajectory tt = trajectory();

        double[] adblExecutionTimeNode = tt.executionTimeNode();

        org.drip.execution.parameters.ArithmeticPriceDynamicsSettings apds =
            lpep.arithmeticPriceDynamicsSettings();

        try {
            dblMarketCoreVolatility = apds.epochVolatility();
        } catch (java.lang.Exception e) {
            e.printStackTrace();

            return null;
        }

        double dblMarketCoreDrift = apds.drift();

        double[] adblHoldings = tt.holdings();

        int iNumTimeNode = adblHoldings.length;
        double dblUnscaledTotalCostVariance = 0.;
        double dblTotalCostMean = 0.5 * dblPermanentLinearImpactParameter * adblHoldings[0] *
            adblHoldings[0];

        for (int i = 1; i < iNumTimeNode; ++i) {
            double dblHoldingsIncrement = adblHoldings[i] - adblHoldings[i - 1];
            double dblTimeInterval = adblExecutionTimeNode[i] - adblExecutionTimeNode[i - 1];
            dblUnscaledTotalCostVariance = dblUnscaledTotalCostVariance + dblTimeInterval * adblHoldings[i] *
                adblHoldings[i];

            dblTotalCostMean = dblTotalCostMean + dblTemporaryOffsetImpactParameter * java.lang.Math.abs
                (dblHoldingsIncrement) + (dblTemporaryLinearImpactParameter - 0.5 *
                    dblPermanentLinearImpactParameter * dblTimeInterval) / dblTimeInterval *
                        dblHoldingsIncrement * dblHoldingsIncrement - dblMarketCoreDrift * dblTimeInterval *
                            adblHoldings[i];
        }

        try {
            return new org.drip.measure.gaussian.R1UnivariateNormal (dblTotalCostMean,
                dblMarketCoreVolatility * java.lang.Math.sqrt (dblUnscaledTotalCostVariance));
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }
}