ContinuousForwardRateEvolver.java
package org.drip.dynamics.lmm;
/*
* -*- 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
* Copyright (C) 2015 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>ContinuousForwardRateEvolver</i> sets up and implements the Multi-Factor No-arbitrage Dynamics of the
* Rates State Quantifiers traced from the Evolution of the Continuously Compounded Forward Rate as
* formulated in:
*
* <br><br>
* <ul>
* <li>
* Goldys, B., M. Musiela, and D. Sondermann (1994): <i>Log-normality of Rates and Term Structure
* Models</i> <b>The University of New South Wales</b>
* </li>
* <li>
* Musiela, M. (1994): <i>Nominal Annual Rates and Log-normal Volatility Structure</i> <b>The
* University of New South Wales</b>
* </li>
* <li>
* Brace, A., D. Gatarek, and M. Musiela (1997): The Market Model of Interest Rate Dynamics
* <i>Mathematical Finance</i> <b>7 (2)</b> 127-155
* </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/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
* <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>
* <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>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ContinuousForwardRateEvolver implements org.drip.dynamics.evolution.PointStateEvolver {
private org.drip.dynamics.hjm.MultiFactorVolatility _mfv = null;
private org.drip.state.identifier.ForwardLabel _lslForward = null;
private org.drip.state.identifier.FundingLabel _lslFunding = null;
private double volatilityRandomDotProduct (
final int iViewDate,
final int iTargetDate,
final int iViewTimeIncrement)
throws java.lang.Exception
{
double dblViewTimeIncrementSQRT = java.lang.Math.sqrt (iViewTimeIncrement);
org.drip.sequence.random.PrincipalFactorSequenceGenerator pfsg = _mfv.msg();
double[] adblMultivariateRandom = pfsg.random();
double dblVolatilityRandomDotProduct = 0.;
int iNumFactor = pfsg.numFactor();
for (int i = 0; i < iNumFactor; ++i)
dblVolatilityRandomDotProduct += _mfv.weightedFactorPointVolatility (i, iViewDate, iTargetDate) *
adblMultivariateRandom[i] * dblViewTimeIncrementSQRT;
return dblVolatilityRandomDotProduct;
}
private double volatilityRandomDotDerivative (
final int iViewDate,
final int iTargetDate,
final int iViewTimeIncrement,
final boolean bTerminal)
throws java.lang.Exception
{
org.drip.function.definition.R1ToR1 pointVolatilityFunctionR1ToR1 = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblX)
throws java.lang.Exception
{
return bTerminal ? volatilityRandomDotProduct (iViewDate, (int) dblX, iViewTimeIncrement) :
volatilityRandomDotProduct ((int) dblX, iTargetDate, iViewTimeIncrement);
}
};
return pointVolatilityFunctionR1ToR1.derivative (bTerminal ? iTargetDate : iViewDate, 1);
}
/**
* ContinuousForwardRateEvolver Constructor
*
* @param lslFunding The Funding Latent State Label
* @param lslForward The Forward Latent State Label
* @param mfv The Multi-Factor Volatility Instance
* @param auInitialInstantaneousForwardRate The Instantaneous Forward Rate Function
*
* @throws java.lang.Exception Thrown if Inputs are Invalid
*/
public ContinuousForwardRateEvolver (
final org.drip.state.identifier.FundingLabel lslFunding,
final org.drip.state.identifier.ForwardLabel lslForward,
final org.drip.dynamics.hjm.MultiFactorVolatility mfv,
final org.drip.function.definition.R1ToR1 auInitialInstantaneousForwardRate)
throws java.lang.Exception
{
if (null == (_lslFunding = lslFunding) || null == (_lslForward = lslForward) || null == (_mfv = mfv))
throw new java.lang.Exception ("ContinuousForwardRateEvolver ctr: Invalid Inputs");
}
/**
* Retrieve the Funding Label
*
* @return The Funding Label
*/
public org.drip.state.identifier.FundingLabel fundingLabel()
{
return _lslFunding;
}
/**
* Retrieve the Forward Label
*
* @return The Forward Label
*/
public org.drip.state.identifier.ForwardLabel forwardLabel()
{
return _lslForward;
}
/**
* Retrieve the Multi-factor Volatility Instance
*
* @return The Multi-factor Volatility Instance
*/
public org.drip.dynamics.hjm.MultiFactorVolatility mfv()
{
return _mfv;
}
@Override public org.drip.dynamics.lmm.ContinuousForwardRateUpdate evolve (
final int iSpotDate,
final int iViewDate,
final int iSpotTimeIncrement,
final org.drip.dynamics.evolution.LSQMPointUpdate lsqmPrev)
{
if (iSpotDate > iViewDate || (null != lsqmPrev && !(lsqmPrev instanceof
org.drip.dynamics.lmm.ContinuousForwardRateUpdate)))
return null;
org.drip.dynamics.lmm.ContinuousForwardRateUpdate bgmPrev =
(org.drip.dynamics.lmm.ContinuousForwardRateUpdate) lsqmPrev;
double dblDContinuousForwardDXTerminalPrev = bgmPrev.dContinuousForwardDXTerminal();
double dblDContinuousForwardDXInitialPrev = bgmPrev.dContinuousForwardDXInitial();
try {
double dblDiscountFactorPrev = bgmPrev.discountFactor();
double dblSpotRateIncrement = dblDContinuousForwardDXInitialPrev * iSpotTimeIncrement +
volatilityRandomDotDerivative (iSpotDate, iViewDate, iSpotTimeIncrement, false);
double dblContinuousForwardIncrement = (dblDContinuousForwardDXTerminalPrev + 0.5 *
_mfv.pointVolatilityModulusDerivative (iSpotDate, iViewDate, 1, true)) * iSpotTimeIncrement +
volatilityRandomDotDerivative (iSpotDate, iViewDate, iSpotTimeIncrement, true);
double dblContinuousForwardRate = bgmPrev.continuousForwardRate() +
dblContinuousForwardIncrement;
double dblSpotRate = bgmPrev.spotRate() + dblSpotRateIncrement;
double dblDiscountFactorIncrement = dblDiscountFactorPrev * ((dblSpotRate -
dblContinuousForwardRate) * iSpotTimeIncrement - volatilityRandomDotProduct (iSpotDate,
iViewDate, iSpotTimeIncrement));
return org.drip.dynamics.lmm.ContinuousForwardRateUpdate.Create (_lslFunding, _lslForward,
iSpotDate, iSpotDate + iSpotTimeIncrement, iViewDate, dblContinuousForwardRate,
dblContinuousForwardIncrement, dblSpotRate, dblSpotRateIncrement, dblDiscountFactorPrev +
dblDiscountFactorIncrement, dblDiscountFactorIncrement,
dblDContinuousForwardDXInitialPrev, dblDContinuousForwardDXTerminalPrev);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Compute the Realized Zero Coupon Bond Forward Price
*
* @param iSpotDate The Spot Date
* @param iForwardDate The Forward Date
* @param iMaturityDate The Maturity Date
* @param dblSpotPrice The Spot Price
* @param dblSpotForwardReinvestmentAccrual The Continuously Re-invested Accruing Bank Account
*
* @return The Realized Zero Coupon Bond Forward Price
*
* @throws java.lang.Exception Thrown if the Inputs are invalid
*/
public double zeroCouponForwardPrice (
final int iSpotDate,
final int iForwardDate,
final int iMaturityDate,
final double dblSpotPrice,
final double dblSpotForwardReinvestmentAccrual)
throws java.lang.Exception
{
if (iSpotDate > iForwardDate || iForwardDate > iMaturityDate ||
!org.drip.numerical.common.NumberUtil.IsValid (dblSpotPrice) ||
!org.drip.numerical.common.NumberUtil.IsValid (dblSpotForwardReinvestmentAccrual))
throw new java.lang.Exception
("ContinuousForwardRateEvolver::zeroCouponForwardPrice => Invalid Inputs");
int iPeriodIncrement = iForwardDate - iSpotDate;
return dblSpotPrice / dblSpotForwardReinvestmentAccrual * java.lang.Math.exp (-1. *
(volatilityRandomDotProduct (iSpotDate, iForwardDate, iPeriodIncrement) + 0.5 * iPeriodIncrement
* _mfv.pointVolatilityModulus (iSpotDate, iForwardDate)));
}
}