BayesianPriceProcess.java

package org.drip.sample.trend;

import org.drip.execution.bayesian.*;
import org.drip.measure.gaussian.R1UnivariateNormal;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * 
 *  This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
 *      libraries targeting analysts and developers
 *      https://lakshmidrip.github.io/DRIP/
 *  
 *  DRIP is composed of four main libraries:
 *  
 *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
 *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
 *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
 *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
 * 
 *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
 *      Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
 *      Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
 *      Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
 *      Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
 * 
 *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
 *      Incorporator, Holdings Constraint, and Transaction Costs.
 * 
 *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
 * 
 *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
 * 
 *  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.
 */

/**
 * BayesianPriceProcess demonstrates the Evolution Process for an Asset Price with a Uncertain (Bayesian)
 *  Drift. The References are:
 * 
 *  - Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs, Journal of Financial Markets 1
 *      1-50.
 * 
 *  - Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions, Journal of Risk 3 (2)
 *      5-39.
 * 
 *  - Brunnermeier, L. K., and L. H. Pedersen (2005): Predatory Trading, Journal of Finance 60 (4) 1825-1863.
 *
 *  - Almgren, R., and J. Lorenz (2006): Bayesian Adaptive Trading with a Daily Cycle, Journal of Trading 1
 *      (4) 38-46.
 * 
 *  - Kissell, R., and R. Malamut (2007): Algorithmic Decision Making Framework, Journal of Trading 1 (1)
 *      12-21.
 * 
 * @author Lakshmi Krishnamurthy
 */

public class BayesianPriceProcess {

    public static final void main (
        final String[] astrArgs)
        throws Exception
    {
        EnvManager.InitEnv ("");

        int iN = 25;
        double dblT = 1.0;
        double dblNu = 1.0;
        double dblS0 = 100.;
        double dblSigma = 1.5;
        double dblAlphaBar = 0.7;

        double dblTime = 0.;
        double dblPrice = dblS0;
        double dblTimeWidth = dblT / iN;

        PriorDriftDistribution pdd = new PriorDriftDistribution (
            dblAlphaBar,
            dblNu
        );

        double[] adblAlpha = pdd.realizedDrift (iN);

        System.out.println();

        System.out.println ("\t|--------------------------------------------------||");

        System.out.println ("\t|  L -> R                                          ||");

        System.out.println ("\t|--------------------------------------------------||");

        System.out.println ("\t|    - Time                                        ||");

        System.out.println ("\t|    - Realized Drift                              ||");

        System.out.println ("\t|    - Realized Price Volatility Swing             ||");

        System.out.println ("\t|    - Realized Price                              ||");

        System.out.println ("\t|    - MAP Drift Estimate                          ||");

        System.out.println ("\t|    - Posterior Drift Volatility                  ||");

        System.out.println ("\t|--------------------------------------------------||");

        for (int i = 0; i < iN; ++i) {
            dblTime = dblTime + dblTimeWidth;

            ConditionalPriceDistribution cpd = new ConditionalPriceDistribution (
                adblAlpha[i],
                dblSigma,
                dblTime
            );

            double dblPriceSwing = cpd.priceVolatilitySwing();

            double dblRealizedPriceChange = adblAlpha[i] * dblTimeWidth + dblPriceSwing;
            dblPrice = dblPrice + dblRealizedPriceChange;

            PriorConditionalCombiner pcc = new PriorConditionalCombiner (
                pdd,
                cpd
            );

            R1UnivariateNormal r1unPosterior = pcc.posteriorDriftDistribution (dblRealizedPriceChange);

            System.out.println (
                "\t| " + FormatUtil.FormatDouble (dblTime, 1, 2, 1.) + " => " +
                FormatUtil.FormatDouble (adblAlpha[i], 1, 2, 1.) + " | " +
                FormatUtil.FormatDouble (dblPriceSwing, 1, 2, 1.) + " | " +
                FormatUtil.FormatDouble (dblPrice, 3, 2, 1.) + " | " +
                FormatUtil.FormatDouble (r1unPosterior.mean(), 1, 2, 1.) + " | " +
                FormatUtil.FormatDouble (Math.sqrt (r1unPosterior.variance()), 1, 2, 1.) + " ||"
            );
        }

        System.out.println ("\t|--------------------------------------------------||");
    }
}