LognormalLIBORVolatility.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
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*
* 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
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* 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>LognormalLIBORVolatility</i> implements the Multi-Factor Log-normal LIBOR Volatility 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 LognormalLIBORVolatility extends org.drip.dynamics.hjm.MultiFactorVolatility {
private int _iSpotDate = java.lang.Integer.MIN_VALUE;
private org.drip.state.identifier.ForwardLabel _lslForward = null;
/**
* LognormalLIBORVolatility Constructor
*
* @param iSpotDate The Spot Date
* @param lslForward The Forward Label
* @param aMSVolatility Array of the Multi-Factor Volatility Surfaces
* @param pfsg Principal Factor Sequence Generator
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public LognormalLIBORVolatility (
final int iSpotDate,
final org.drip.state.identifier.ForwardLabel lslForward,
final org.drip.analytics.definition.MarketSurface[] aMSVolatility,
final org.drip.sequence.random.PrincipalFactorSequenceGenerator pfsg)
throws java.lang.Exception
{
super (aMSVolatility, pfsg);
if (null == (_lslForward = lslForward))
throw new java.lang.Exception ("LognormalLIBORVolatility ctr: Invalid Inputs");
_iSpotDate = iSpotDate;
}
/**
* Retrieve the Spot Date
*
* @return The Spot Date
*/
public int spotDate()
{
return _iSpotDate;
}
/**
* Retrieve the Forward Label
*
* @return The Forward Label
*/
public org.drip.state.identifier.ForwardLabel forwardLabel()
{
return _lslForward;
}
/**
* Compute the Constraint in the Difference in the Volatility of the Continuously Compounded Forward Rate
* between the Target Date and the Target Date + Forward Tenor
*
* @param fc The Forward Curve Instance
* @param iTargetDate The Target Date
*
* @return The Constraint in the Difference in the Volatility of the Continuously Compounded Forward Rate
*/
public double[] continuousForwardVolatilityConstraint (
final org.drip.state.forward.ForwardCurve fc,
final int iTargetDate)
{
if (null == fc || iTargetDate <= _iSpotDate) return null;
java.lang.String strTenor = _lslForward.tenor();
org.drip.analytics.definition.MarketSurface[] aMS = volatilitySurface();
try {
double dblLIBORDCF = fc.forward (new org.drip.analytics.date.JulianDate (iTargetDate).addTenor
(strTenor)) * org.drip.analytics.support.Helper.TenorToYearFraction (strTenor);
int iNumSurface = aMS.length;
double dblConstraintWeight = dblLIBORDCF / (1. + dblLIBORDCF);
double[] adblContinuousForwardVolatilityConstraint = new double[iNumSurface];
for (int i = 0; i < iNumSurface; ++i)
adblContinuousForwardVolatilityConstraint[i] = dblConstraintWeight * aMS[i].node (_iSpotDate,
iTargetDate);
return adblContinuousForwardVolatilityConstraint;
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Compute the Volatility of the Continuously Compounded Forward Rate Up to the Target Date
*
* @param iTargetDate The Target Date
* @param fc The Forward Curve Instance
*
* @return The Volatility of the Continuously Compounded Forward Rate Up to the Target Date
*/
public double[] continuousForwardVolatility (
final int iTargetDate,
final org.drip.state.forward.ForwardCurve fc)
{
if (iTargetDate <= _iSpotDate || null == fc) return null;
org.drip.sequence.random.PrincipalFactorSequenceGenerator pfsg = msg();
int iNumFactor = pfsg.numFactor();
boolean bLoop = true;
int iEndDate = _iSpotDate;
double dblTenorDCF = java.lang.Double.NaN;
double[] adblContinuousForwardVolatility = new double[iNumFactor];
java.lang.String strTenor = _lslForward.tenor();
try {
dblTenorDCF = org.drip.analytics.support.Helper.TenorToYearFraction (strTenor);
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
for (int i = 0; i < iNumFactor; ++i)
adblContinuousForwardVolatility[i] = 0.;
double[] adblFactorPointVolatility = factorPointVolatility (_iSpotDate, iEndDate);
while (bLoop) {
try {
if ((iEndDate = new org.drip.analytics.date.JulianDate (iEndDate).addTenor
(strTenor).julian()) > iTargetDate)
bLoop = false;
double dblLIBORTenorDCF = fc.forward (iEndDate) * dblTenorDCF;
double dblLIBORLognormalVolatilityScaler = dblLIBORTenorDCF / (1. + dblLIBORTenorDCF);
for (int i = 0; i < iNumFactor; ++i)
adblContinuousForwardVolatility[i] += dblLIBORLognormalVolatilityScaler *
adblFactorPointVolatility[i];
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
}
return adblContinuousForwardVolatility;
}
/**
* Compute the Volatility of the Continuously Compounded Forward Rate Up to the Target Date
*
* @param iTargetDate The Target Date
* @param dc The Discount Curve Instance
*
* @return The Volatility of the Continuously Compounded Forward Rate Up to the Target Date
*/
public double[] continuousForwardVolatility (
final int iTargetDate,
final org.drip.state.discount.MergedDiscountForwardCurve dc)
{
if (iTargetDate <= _iSpotDate || null == dc) return null;
org.drip.sequence.random.PrincipalFactorSequenceGenerator pfsg = msg();
int iNumFactor = pfsg.numFactor();
boolean bLoop = true;
int iStartDate = _iSpotDate;
double dblTenorDCF = java.lang.Double.NaN;
double[] adblContinuousForwardVolatility = new double[iNumFactor];
java.lang.String strTenor = _lslForward.tenor();
try {
dblTenorDCF = org.drip.analytics.support.Helper.TenorToYearFraction (strTenor);
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
for (int i = 0; i < iNumFactor; ++i)
adblContinuousForwardVolatility[i] = 0.;
double[] adblFactorPointVolatility = factorPointVolatility (_iSpotDate, iStartDate);
while (bLoop) {
try {
double dblLIBORTenorDCF = dc.libor (iStartDate, strTenor) * dblTenorDCF;
double dblLIBORLognormalVolatilityScaler = dblLIBORTenorDCF / (1. + dblLIBORTenorDCF);
for (int i = 0; i < iNumFactor; ++i)
adblContinuousForwardVolatility[i] += dblLIBORLognormalVolatilityScaler *
adblFactorPointVolatility[i];
if ((iStartDate = new org.drip.analytics.date.JulianDate (iStartDate).addTenor
(strTenor).julian()) > iTargetDate)
bLoop = false;
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
}
return adblContinuousForwardVolatility;
}
/**
* Multi-Factor Cross Volatility Integral
*
* @param iForwardDate1 Forward Date #1
* @param iForwardDate2 Forward Date #2
* @param iTerminalDate The Terminal Date
*
* @return The Multi-Factor Cross Volatility Integral
*
* @throws java.lang.Exception Thrown if the Multi-Factor Cross Volatility Integral cannot be computed
*/
public double crossVolatilityIntegralProduct (
final int iForwardDate1,
final int iForwardDate2,
final int iTerminalDate)
throws java.lang.Exception
{
if (iForwardDate1 < iTerminalDate || iForwardDate2 < iTerminalDate)
throw new java.lang.Exception
("LognormalLIBORVolatility::crossVolatilityIntegralProduct => Invalid Inputs");
org.drip.function.definition.R1ToR1 crossVolR1ToR1 = new org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblDate)
throws java.lang.Exception
{
double dblCrossVolProduct = 0.;
int iNumFactor = msg().numFactor();
for (int iFactorIndex = 0; iFactorIndex < iNumFactor; ++iFactorIndex)
dblCrossVolProduct += factorPointVolatility (iFactorIndex, (int) dblDate, iForwardDate1)
* factorPointVolatility (iFactorIndex, (int) dblDate, iForwardDate2);
return dblCrossVolProduct;
}
};
return crossVolR1ToR1.integrate (_iSpotDate, iTerminalDate);
}
}