/*
Copyright (C) 2008 Richard Gomes
This source code is release under the BSD License.
This file is part of JQuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://jquantlib.org/
JQuantLib is free software: you can redistribute it and/or modify it
under the terms of the JQuantLib license. You should have received a
copy of the license along with this program; if not, please email
. The license is also available online at
.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
JQuantLib is based on QuantLib. http://quantlib.org/
When applicable, the original copyright notice follows this notice.
*/
/*
Copyright (C) 2003 Ferdinando Ametrano
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
. The license is also available online at
.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
package org.jquantlib.termstructures.volatilities;
import org.jquantlib.QL;
import org.jquantlib.daycounters.DayCounter;
import org.jquantlib.quotes.Handle;
import org.jquantlib.quotes.Quote;
import org.jquantlib.quotes.SimpleQuote;
import org.jquantlib.termstructures.BlackVolTermStructure;
import org.jquantlib.termstructures.LocalVolTermStructure;
import org.jquantlib.termstructures.TermStructure;
import org.jquantlib.termstructures.YieldTermStructure;
import org.jquantlib.time.Date;
import org.jquantlib.util.PolymorphicVisitor;
import org.jquantlib.util.Visitor;
/**
* Local volatility surface derived from a Black vol surface
*
* For details about this implementation refer to "Stochastic Volatility and
* Local Volatility" in "Case Studies and Financial Modelling Course Notes," by
* Jim Gatheral, Fall Term, 2003
*
* @see This article
*
* @author Richard Gomes
*/
// TODO: this class is untested, probably unreliable.
public class LocalVolSurface extends LocalVolTermStructure {
private final Handle blackTS_;
private final Handle riskFreeTS_;
private final Handle dividendTS_;
private final Handle underlying_;
public LocalVolSurface(
final Handle blackTS,
final Handle riskFreeTS,
final Handle dividendTS,
final Handle underlying) {
super(blackTS.currentLink().calendar(),
blackTS.currentLink().businessDayConvention(),
blackTS.currentLink().dayCounter());
this.blackTS_ = blackTS;
this.riskFreeTS_ = riskFreeTS;
this.dividendTS_ = dividendTS;
this.underlying_ = underlying;
this.blackTS_.addObserver(this);
this.riskFreeTS_.addObserver(this);
this.dividendTS_.addObserver(this);
this.underlying_.addObserver(this);
}
public LocalVolSurface(
final Handle blackTS,
final Handle riskFreeTS,
final Handle dividendTS,
final /*@Real*/ double underlying) {
super(blackTS.currentLink().calendar(),
blackTS.currentLink().businessDayConvention(),
blackTS.currentLink().dayCounter());
this.blackTS_ = blackTS;
this.riskFreeTS_ = riskFreeTS;
this.dividendTS_ = dividendTS;
this.underlying_ = new Handle(new SimpleQuote(underlying));
this.blackTS_.addObserver(this);
this.riskFreeTS_.addObserver(this);
this.dividendTS_.addObserver(this);
}
//
// Overrides LocalVolTermStructure
//
@Override
public final Date referenceDate() {
return this.blackTS_.currentLink().referenceDate();
}
@Override
public final DayCounter dayCounter() {
return this.blackTS_.currentLink().dayCounter();
}
@Override
public final Date maxDate() {
return blackTS_.currentLink().maxDate();
}
@Override
public final /*@Real*/ double minStrike() {
return blackTS_.currentLink().minStrike();
}
@Override
public final /*@Real*/ double maxStrike() {
return blackTS_.currentLink().maxStrike();
}
@Override
protected final /*@Volatility*/ double localVolImpl(
final /*@Time*/ double time,
final /*@Real*/ double underlyingLevel) {
// obtain local copies of objects
final Quote u = underlying_.currentLink();
final YieldTermStructure dTS = dividendTS_.currentLink();
final YieldTermStructure rTS = riskFreeTS_.currentLink();
final BlackVolTermStructure bTS = blackTS_.currentLink();
final double forwardValue = u.value() * ( dTS.discount(time, true) / rTS.discount(time, true) );
// strike derivatives
/*@Real*/ double strike;
/*@Real*/ double strikem;
/*@Real*/ double strikep;
double y, dy;
double w, wp, wm, dwdy, d2wdy2;
strike = underlyingLevel;
y = Math.log(strike / forwardValue);
dy = ((y != 0.0) ? y * 0.000001 : 0.000001);
strikep = strike * Math.exp(dy);
strikem = strike / Math.exp(dy);
w = bTS.blackVariance(time, strike, true);
wp = bTS.blackVariance(time, strikep, true);
wm = bTS.blackVariance(time, strikem, true);
dwdy = (wp - wm) / (2.0 * dy);
d2wdy2 = (wp - 2.0 * w + wm) / (dy * dy);
// time derivative
/*@Time*/ final double t = time;
/*@Time*/ double dt;
double wpt, wmt, dwdt;
if (t == 0.0) {
dt = 0.0001;
wpt = bTS.blackVariance(/*@Time*/ (t + dt), strike, true);
QL.require(wpt >= w , "decreasing variance at strike"); // TODO: message
dwdt = (wpt - w) / dt;
} else {
dt = Math.min(0.0001, t / 2.0);
wpt = bTS.blackVariance(/*@Time*/ (t + dt), strike, true);
wmt = bTS.blackVariance(/*@Time*/ (t - dt), strike, true);
QL.ensure(wpt >= w , "decreasing variance at strike"); // TODO: message
QL.ensure(w >= wmt , "decreasing variance at strike"); // TODO: message
dwdt = (wpt - wmt) / (2.0 * dt);
}
if (dwdy == 0.0 && d2wdy2 == 0.0)
return Math.sqrt(dwdt);
else {
final double den1 = 1.0 - y / w * dwdy;
final double den2 = 0.25 * (-0.25 - 1.0 / w + y * y / w / w) * dwdy * dwdy;
final double den3 = 0.5 * d2wdy2;
final double den = den1 + den2 + den3;
final double result = dwdt / den;
QL.ensure(result >= 0.0 , "negative local vol^2 at strike); the black vol surface is not smooth enough"); // TODO: message
return Math.sqrt(result);
// TODO: code review :: please verify against QL/C++ code
// commented out at original source QuantLib
// return std::sqrt(dwdt / (1.0 - y/w*dwdy +
// 0.25*(-0.25 - 1.0/w + y*y/w/w)*dwdy*dwdy + 0.5*d2wdy2));
}
}
//
// implements PolymorphicVisitable
//
@Override
public void accept(final PolymorphicVisitor pv) {
final Visitor v = (pv!=null) ? pv.visitor(this.getClass()) : null;
if (v != null) {
v.visit(this);
} else {
super.accept(pv);
}
}
}
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