ContinuousForwardRateEvolver.java

  1. package org.drip.dynamics.lmm;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  14.  * 
  15.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  16.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  17.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  18.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  19.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  20.  *      and computational support.
  21.  *  
  22.  *      https://lakshmidrip.github.io/DROP/
  23.  *  
  24.  *  DROP is composed of three modules:
  25.  *  
  26.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  27.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  28.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  29.  * 
  30.  *  DROP Product Core implements libraries for the following:
  31.  *  - Fixed Income Analytics
  32.  *  - Loan Analytics
  33.  *  - Transaction Cost Analytics
  34.  * 
  35.  *  DROP Portfolio Core implements libraries for the following:
  36.  *  - Asset Allocation Analytics
  37.  *  - Asset Liability Management Analytics
  38.  *  - Capital Estimation Analytics
  39.  *  - Exposure Analytics
  40.  *  - Margin Analytics
  41.  *  - XVA Analytics
  42.  * 
  43.  *  DROP Computational Core implements libraries for the following:
  44.  *  - Algorithm Support
  45.  *  - Computation Support
  46.  *  - Function Analysis
  47.  *  - Model Validation
  48.  *  - Numerical Analysis
  49.  *  - Numerical Optimizer
  50.  *  - Spline Builder
  51.  *  - Statistical Learning
  52.  * 
  53.  *  Documentation for DROP is Spread Over:
  54.  * 
  55.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  56.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  57.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  58.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  59.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  60.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  61.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  62.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  63.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  64.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  65.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  66.  * 
  67.  *  Licensed under the Apache License, Version 2.0 (the "License");
  68.  *      you may not use this file except in compliance with the License.
  69.  *   
  70.  *  You may obtain a copy of the License at
  71.  *      http://www.apache.org/licenses/LICENSE-2.0
  72.  *  
  73.  *  Unless required by applicable law or agreed to in writing, software
  74.  *      distributed under the License is distributed on an "AS IS" BASIS,
  75.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  76.  *  
  77.  *  See the License for the specific language governing permissions and
  78.  *      limitations under the License.
  79.  */

  81. /**
  82.  * <i>ContinuousForwardRateEvolver</i> sets up and implements the Multi-Factor No-arbitrage Dynamics of the
  83.  * Rates State Quantifiers traced from the Evolution of the Continuously Compounded Forward Rate as
  84.  * formulated in:
  85.  *
  86.  *  <br><br>
  87.  *  <ul>
  88.  *      <li>
  89.  *          Goldys, B., M. Musiela, and D. Sondermann (1994): <i>Log-normality of Rates and Term Structure
  90.  *              Models</i> <b>The University of New South Wales</b>
  91.  *      </li>
  92.  *      <li>
  93.  *          Musiela, M. (1994): <i>Nominal Annual Rates and Log-normal Volatility Structure</i> <b>The
  94.  *              University of New South Wales</b>
  95.  *      </li>
  96.  *      <li>
  97.  *          Brace, A., D. Gatarek, and M. Musiela (1997): The Market Model of Interest Rate Dynamics
  98.  *              <i>Mathematical Finance</i> <b>7 (2)</b> 127-155
  99.  *      </li>
  100.  *  </ul>
  101.  *
  102.  *  <br><br>
  103.  *  <ul>
  104.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  105.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
  106.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/README.md">HJM, Hull White, LMM, and SABR Dynamic Evolution Models</a></li>
  107.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/lmm/README.md">LMM Based Latent State Evolution</a></li>
  108.  *  </ul>
  109.  *  
  110.  * @author Lakshmi Krishnamurthy
  111.  */

  113. public class ContinuousForwardRateEvolver implements org.drip.dynamics.evolution.PointStateEvolver {
  114.     private org.drip.dynamics.hjm.MultiFactorVolatility _mfv = null;
  115.     private org.drip.state.identifier.ForwardLabel _lslForward = null;
  116.     private org.drip.state.identifier.FundingLabel _lslFunding = null;

  118.     private double volatilityRandomDotProduct (
  119.         final int iViewDate,
  120.         final int iTargetDate,
  121.         final int iViewTimeIncrement)
  122.         throws java.lang.Exception
  123.     {
  124.         double dblViewTimeIncrementSQRT = java.lang.Math.sqrt (iViewTimeIncrement);

  126.         org.drip.sequence.random.PrincipalFactorSequenceGenerator pfsg = _mfv.msg();

  128.         double[] adblMultivariateRandom = pfsg.random();

  130.         double dblVolatilityRandomDotProduct = 0.;

  132.         int iNumFactor = pfsg.numFactor();

  134.         for (int i = 0; i < iNumFactor; ++i)
  135.             dblVolatilityRandomDotProduct += _mfv.weightedFactorPointVolatility (i, iViewDate, iTargetDate) *
  136.                 adblMultivariateRandom[i] * dblViewTimeIncrementSQRT;

  138.         return dblVolatilityRandomDotProduct;
  139.     }

  141.     private double volatilityRandomDotDerivative (
  142.         final int iViewDate,
  143.         final int iTargetDate,
  144.         final int iViewTimeIncrement,
  145.         final boolean bTerminal)
  146.         throws java.lang.Exception
  147.     {
  148.         org.drip.function.definition.R1ToR1 pointVolatilityFunctionR1ToR1 = new
  149.             org.drip.function.definition.R1ToR1 (null) {
  150.             @Override public double evaluate (
  151.                 final double dblX)
  152.                 throws java.lang.Exception
  153.             {
  154.                 return bTerminal ? volatilityRandomDotProduct (iViewDate, (int) dblX, iViewTimeIncrement) :
  155.                     volatilityRandomDotProduct ((int) dblX, iTargetDate, iViewTimeIncrement);
  156.             }
  157.         };

  159.         return pointVolatilityFunctionR1ToR1.derivative (bTerminal ? iTargetDate : iViewDate, 1);
  160.     }

  162.     /**
  163.      * ContinuousForwardRateEvolver Constructor
  164.      * 
  165.      * @param lslFunding The Funding Latent State Label
  166.      * @param lslForward The Forward Latent State Label
  167.      * @param mfv The Multi-Factor Volatility Instance
  168.      * @param auInitialInstantaneousForwardRate The Instantaneous Forward Rate Function
  169.      * 
  170.      * @throws java.lang.Exception Thrown if Inputs are Invalid
  171.      */

  173.     public ContinuousForwardRateEvolver (
  174.         final org.drip.state.identifier.FundingLabel lslFunding,
  175.         final org.drip.state.identifier.ForwardLabel lslForward,
  176.         final org.drip.dynamics.hjm.MultiFactorVolatility mfv,
  177.         final org.drip.function.definition.R1ToR1 auInitialInstantaneousForwardRate)
  178.         throws java.lang.Exception
  179.     {
  180.         if (null == (_lslFunding = lslFunding) || null == (_lslForward = lslForward) || null == (_mfv = mfv))
  181.             throw new java.lang.Exception ("ContinuousForwardRateEvolver ctr: Invalid Inputs");
  182.     }

  184.     /**
  185.      * Retrieve the Funding Label
  186.      * 
  187.      * @return The Funding Label
  188.      */

  190.     public org.drip.state.identifier.FundingLabel fundingLabel()
  191.     {
  192.         return _lslFunding;
  193.     }

  195.     /**
  196.      * Retrieve the Forward Label
  197.      * 
  198.      * @return The Forward Label
  199.      */

  201.     public org.drip.state.identifier.ForwardLabel forwardLabel()
  202.     {
  203.         return _lslForward;
  204.     }

  206.     /**
  207.      * Retrieve the Multi-factor Volatility Instance
  208.      * 
  209.      * @return The Multi-factor Volatility Instance
  210.      */

  212.     public org.drip.dynamics.hjm.MultiFactorVolatility mfv()
  213.     {
  214.         return _mfv;
  215.     }

  217.     @Override public org.drip.dynamics.lmm.ContinuousForwardRateUpdate evolve (
  218.         final int iSpotDate,
  219.         final int iViewDate,
  220.         final int iSpotTimeIncrement,
  221.         final org.drip.dynamics.evolution.LSQMPointUpdate lsqmPrev)
  222.     {
  223.         if (iSpotDate > iViewDate || (null != lsqmPrev && !(lsqmPrev instanceof
  224.             org.drip.dynamics.lmm.ContinuousForwardRateUpdate)))
  225.             return null;

  227.         org.drip.dynamics.lmm.ContinuousForwardRateUpdate bgmPrev =
  228.             (org.drip.dynamics.lmm.ContinuousForwardRateUpdate) lsqmPrev;

  230.         double dblDContinuousForwardDXTerminalPrev = bgmPrev.dContinuousForwardDXTerminal();

  232.         double dblDContinuousForwardDXInitialPrev = bgmPrev.dContinuousForwardDXInitial();

  234.         try {
  235.             double dblDiscountFactorPrev = bgmPrev.discountFactor();

  237.             double dblSpotRateIncrement = dblDContinuousForwardDXInitialPrev * iSpotTimeIncrement +
  238.                 volatilityRandomDotDerivative (iSpotDate, iViewDate, iSpotTimeIncrement, false);

  240.             double dblContinuousForwardIncrement = (dblDContinuousForwardDXTerminalPrev + 0.5 *
  241.                 _mfv.pointVolatilityModulusDerivative (iSpotDate, iViewDate, 1, true)) * iSpotTimeIncrement +
  242.                     volatilityRandomDotDerivative (iSpotDate, iViewDate, iSpotTimeIncrement, true);

  244.             double dblContinuousForwardRate = bgmPrev.continuousForwardRate() +
  245.                 dblContinuousForwardIncrement;

  247.             double dblSpotRate = bgmPrev.spotRate() + dblSpotRateIncrement;

  249.             double dblDiscountFactorIncrement = dblDiscountFactorPrev * ((dblSpotRate -
  250.                 dblContinuousForwardRate) * iSpotTimeIncrement - volatilityRandomDotProduct (iSpotDate,
  251.                     iViewDate, iSpotTimeIncrement));

  253.             return org.drip.dynamics.lmm.ContinuousForwardRateUpdate.Create (_lslFunding, _lslForward,
  254.                 iSpotDate, iSpotDate + iSpotTimeIncrement, iViewDate, dblContinuousForwardRate,
  255.                     dblContinuousForwardIncrement, dblSpotRate, dblSpotRateIncrement, dblDiscountFactorPrev +
  256.                         dblDiscountFactorIncrement, dblDiscountFactorIncrement,
  257.                             dblDContinuousForwardDXInitialPrev, dblDContinuousForwardDXTerminalPrev);
  258.         } catch (java.lang.Exception e) {
  259.             e.printStackTrace();
  260.         }

  262.         return null;
  263.     }

  265.     /**
  266.      * Compute the Realized Zero Coupon Bond Forward Price
  267.      * 
  268.      * @param iSpotDate The Spot Date
  269.      * @param iForwardDate The Forward Date
  270.      * @param iMaturityDate The Maturity Date
  271.      * @param dblSpotPrice The Spot Price
  272.      * @param dblSpotForwardReinvestmentAccrual The Continuously Re-invested Accruing Bank Account
  273.      * 
  274.      * @return The Realized Zero Coupon Bond Forward Price
  275.      * 
  276.      * @throws java.lang.Exception Thrown if the Inputs are invalid
  277.      */

  279.     public double zeroCouponForwardPrice (
  280.         final int iSpotDate,
  281.         final int iForwardDate,
  282.         final int iMaturityDate,
  283.         final double dblSpotPrice,
  284.         final double dblSpotForwardReinvestmentAccrual)
  285.         throws java.lang.Exception
  286.     {
  287.         if (iSpotDate > iForwardDate || iForwardDate > iMaturityDate ||
  288.             !org.drip.numerical.common.NumberUtil.IsValid (dblSpotPrice) ||
  289.                 !org.drip.numerical.common.NumberUtil.IsValid (dblSpotForwardReinvestmentAccrual))
  290.             throw new java.lang.Exception
  291.                 ("ContinuousForwardRateEvolver::zeroCouponForwardPrice => Invalid Inputs");

  293.         int iPeriodIncrement = iForwardDate - iSpotDate;

  295.         return dblSpotPrice / dblSpotForwardReinvestmentAccrual * java.lang.Math.exp (-1. *
  296.             (volatilityRandomDotProduct (iSpotDate, iForwardDate, iPeriodIncrement) + 0.5 * iPeriodIncrement
  297.                 * _mfv.pointVolatilityModulus (iSpotDate, iForwardDate)));
  298.     }
  299. }
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