/*
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, 2004, 2005, 2006 Ferdinando Ametrano
Copyright (C) 2006 StatPro Italia srl
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.pricingengines;
import org.jquantlib.QL;
import org.jquantlib.instruments.AssetOrNothingPayoff;
import org.jquantlib.instruments.CashOrNothingPayoff;
import org.jquantlib.instruments.GapPayoff;
import org.jquantlib.instruments.Option;
import org.jquantlib.instruments.Payoff;
import org.jquantlib.instruments.PlainVanillaPayoff;
import org.jquantlib.instruments.StrikedTypePayoff;
import org.jquantlib.lang.exceptions.LibraryException;
import org.jquantlib.math.Constants;
import org.jquantlib.math.distributions.CumulativeNormalDistribution;
import org.jquantlib.util.PolymorphicVisitor;
import org.jquantlib.util.Visitor;
/**
* Black 1976 calculator class
*
* @note BUG: When the variance is null, division by zero occur during
* the calculation of delta, delta forward, gamma, gamma forward, rho,
* dividend rho, vega, and strike sensitivity.
*
* @author Richard Gomes
*/
// FIXME When the variance is null, division by zero occur during calculations
// TODO: write test cases, including a situation when variance is zero
public class BlackCalculator {
//
// private final fields
//
private final /* @Real */ double strike;
private final /* @Real */ double forward;
private final /* @StdDev */ double stdDev;
private final /* @DiscountFactor */ double discount;
private final /* @Variance */ double variance;
private final double dX_dS;
private final double n_d1, cum_d1, n_d2, cum_d2;
//
// private fields
//
private double D1, D2;
private double alpha, beta;
private double dAlpha_dD1, dBeta_dD2;
private double x;
private double dx_dStrike;
//
// public constructors
//
public BlackCalculator(final StrikedTypePayoff payoff, final double forward, final double stdDev) {
this(payoff, forward, stdDev, 1.0);
}
public BlackCalculator(final StrikedTypePayoff payoff, final double forward, final double stdDev, final double discount) {
this.strike = payoff.strike();
this.forward = forward;
this.stdDev = stdDev;
this.discount = discount;
this.variance = stdDev * stdDev;
QL.require(forward > 0.0 , "positive forward value required");
QL.require(stdDev >= 0.0 , "non-negative standard deviation required");
QL.require(discount > 0.0 , "positive discount required");
if (stdDev >= Constants.QL_EPSILON) {
if (strike == 0.0) {
n_d1 = 0.0;
n_d2 = 0.0;
cum_d1 = 1.0;
cum_d2 = 1.0;
} else {
D1 = Math.log(forward / strike) / stdDev + 0.5 * stdDev;
D2 = D1 - stdDev;
final CumulativeNormalDistribution f = new CumulativeNormalDistribution();
cum_d1 = f.op(D1);
cum_d2 = f.op(D2);
n_d1 = f.derivative(D1);
n_d2 = f.derivative(D2);
}
} else {
if (forward > strike) {
cum_d1 = 1.0;
cum_d2 = 1.0;
} else {
cum_d1 = 0.0;
cum_d2 = 0.0;
}
n_d1 = 0.0;
n_d2 = 0.0;
}
x = strike;
dx_dStrike = 1.0;
// the following one will probably disappear as soon as
// super-share will be properly handled
dX_dS = 0.0;
// this part is always executed.
// in case of plain-vanilla payoffs, it is also the only part
// which is executed.
final Option.Type optionType = payoff.optionType();
if (optionType == Option.Type.Call) {
alpha = cum_d1;// N(d1)
dAlpha_dD1 = n_d1;// n(d1)
beta = -cum_d2;// -N(d2)
dBeta_dD2 = -n_d2;// -n(d2)
} else if (optionType == Option.Type.Put) {
alpha = -1.0 + cum_d1;// -N(-d1)
dAlpha_dD1 = n_d1;// n( d1)
beta = 1.0 - cum_d2;// N(-d2)
dBeta_dD2 = -n_d2;// -n( d2)
} else
throw new LibraryException("invalid option type"); // TODO: message
// now dispatch on type.
final Calculator calc = new Calculator(this);
payoff.accept(calc);
}
//
// public methods
//
public/* @Real */double value() /* @ReadOnly */{
/* @Real */final double result = discount * (forward * alpha + x * beta);
return result;
}
/**
* Sensitivity to change in the underlying spot price.
*/
public/* @Real */double delta(final double spot) /* @ReadOnly */{
QL.require(spot > 0.0 , "positive spot value required");
final double DforwardDs = forward / spot;
final double temp = stdDev * spot;
final double DalphaDs = dAlpha_dD1 / temp;
final double DbetaDs = dBeta_dD2 / temp;
final double temp2 = DalphaDs * forward + alpha * DforwardDs + DbetaDs * x + beta * dX_dS;
return discount * temp2;
}
/**
* Sensitivity to change in the underlying forward price.
*/
public/* @Real */double deltaForward() /* @ReadOnly */{
final double temp = stdDev * forward;
final double DalphaDforward = dAlpha_dD1 / temp;
final double DbetaDforward = dBeta_dD2 / temp;
final double temp2 = DalphaDforward * forward + alpha + DbetaDforward * x;
// DXDforward = 0.0; // commented in the source QuantLib
return discount * temp2;
}
/**
* Sensitivity in percent to a percent change in the underlying spot price.
*/
public double elasticity(final double spot) /* @ReadOnly */{
final double val = value();
final double del = delta(spot);
if (val > Constants.QL_EPSILON)
return del / val * spot;
else if (Math.abs(del) < Constants.QL_EPSILON)
return 0.0;
else if (del > 0.0)
return Double.MAX_VALUE;
else
return Double.MIN_VALUE;
}
/**
* Sensitivity in percent to a percent change in the underlying forward
* price.
*/
public double elasticityForward() /* @ReadOnly */{
final double val = value();
final double del = deltaForward();
if (val > Constants.QL_EPSILON)
return del / val * forward;
else if (Math.abs(del) < Constants.QL_EPSILON)
return 0.0;
else if (del > 0.0)
return Double.MAX_VALUE;
else
return Double.MIN_VALUE;
}
/**
* Second order derivative with respect to change in the underlying spot
* price.
*/
public double gamma(final double spot) /* @ReadOnly */{
QL.require(spot > 0.0 , "positive spot value required");
final double DforwardDs = forward / spot;
final double temp = stdDev * spot;
final double DalphaDs = dAlpha_dD1 / temp;
final double DbetaDs = dBeta_dD2 / temp;
final double D2alphaDs2 = -DalphaDs / spot * (1 + D1 / stdDev);
final double D2betaDs2 = -DbetaDs / spot * (1 + D2 / stdDev);
final double temp2 = D2alphaDs2 * forward + 2.0 * DalphaDs * DforwardDs + D2betaDs2 * x + 2.0 * DbetaDs * dX_dS;
return discount * temp2;
}
/**
* Second order derivative with respect to change in the underlying forward
* price.
*/
public double gammaForward() /* @ReadOnly */{
final double temp = stdDev * forward;
final double DalphaDforward = dAlpha_dD1 / temp;
final double DbetaDforward = dBeta_dD2 / temp;
final double D2alphaDforward2 = -DalphaDforward / forward * (1 + D1 / stdDev);
final double D2betaDforward2 = -DbetaDforward / forward * (1 + D2 / stdDev);
final double temp2 = D2alphaDforward2 * forward + 2.0 * DalphaDforward + D2betaDforward2 * x;
// DXDforward = 0.0; // commented in the source QuantLib
return discount * temp2;
}
/**
* Sensitivity to time to maturity.
*/
public double theta(final double spot, final/* @Time */double maturity) /* @ReadOnly */{
QL.require(maturity > 0.0 , "non negative maturity required");
if (maturity == 0.0) return 0.0;
// TODO: code review :: please verify against QL/C++ code
// =====================================================================
//
// *** The following code is commented out in QuantLib ***
//
// vol = stdDev_ / std::sqrt(maturity);
// rate = -std::log(discount_)/maturity;
// dividendRate = -std::log(forward_ / spot * discount_)/maturity;
// return rate*value() - (rate-dividendRate)*spot*delta(spot) - 0.5*vol*vol*spot*spot*gamma(spot);
// =====================================================================
return -(Math.log(discount) * value() + Math.log(forward / spot) * spot * delta(spot) + 0.5 * variance * spot * spot * gamma(spot)) / maturity;
}
/**
* Sensitivity to time to maturity per day, assuming 365 day per year.
*/
public double thetaPerDay(final double spot, /* @Time */final double maturity) /* @ReadOnly */{
return theta(spot, maturity) / 365.0;
}
/**
* Sensitivity to volatility.
*/
public double vega(final/* @Time */double maturity) /* @ReadOnly */{
QL.require(maturity >= 0.0 , "negative maturity not allowed");
final double temp = Math.log(strike / forward) / variance;
// actually DalphaDsigma / SQRT(T)
final double DalphaDsigma = dAlpha_dD1 * (temp + 0.5);
final double DbetaDsigma = dBeta_dD2 * (temp - 0.5);
final double temp2 = DalphaDsigma * forward + DbetaDsigma * x;
return discount * Math.sqrt(maturity) * temp2;
}
/**
* Sensitivity to discounting rate.
*/
public double rho(final/* @Time */double maturity) /* @ReadOnly */{
QL.require(maturity >= 0.0 , "negative maturity not allowed");
// actually DalphaDr / T
final double DalphaDr = dAlpha_dD1 / stdDev;
final double DbetaDr = dBeta_dD2 / stdDev;
final double temp = DalphaDr * forward + alpha * forward + DbetaDr * x;
return maturity * (discount * temp - value());
}
/**
* Sensitivity to dividend/growth rate.
*/
public double dividendRho(final/* @Time */double maturity) /* @ReadOnly */{
QL.require(maturity >= 0.0 , "negative maturity not allowed");
// actually DalphaDq / T
final double DalphaDq = -dAlpha_dD1 / stdDev;
final double DbetaDq = -dBeta_dD2 / stdDev;
final double temp = DalphaDq * forward - alpha * forward + DbetaDq * x;
return maturity * discount * temp;
}
/**
* Probability of being in the money in the bond martingale measure, i.e.
* N(d2).
*
*
* It is a risk-neutral probability, not the real world one.
*/
public double itmCashProbability() /* @ReadOnly */{
return cum_d2;
}
/**
* Probability of being in the money in the asset martingale measure, i.e.
* N(d1).
*
*
* It is a risk-neutral probability, not the real world one.
*/
public double itmAssetProbability() /* @ReadOnly */{
return cum_d1;
}
/**
* Sensitivity to strike.
*/
public double strikeSensitivity() /* @ReadOnly */{
final double temp = stdDev * strike;
final double DalphaDstrike = -dAlpha_dD1 / temp;
final double DbetaDstrike = -dBeta_dD2 / temp;
final double temp2 = DalphaDstrike * forward + DbetaDstrike * x + beta * dx_dStrike;
return discount * temp2;
}
public double alpha() /* @ReadOnly */{
return alpha;
}
public double beta() /* @ReadOnly */{
return beta;
}
//
// inner classes
//
private static class Calculator implements PolymorphicVisitor {
// TODO: refactor messages?
private static final String INVALID_OPTION_TYPE = "invalid option type";
private static final String INVALID_PAYOFF_TYPE = "invalid payoff type";
//
// private fields
//
private final BlackCalculator black;
//
// public constructors
//
public Calculator(final BlackCalculator black) {
this.black = black;
}
//
// implements PolymorphicVisitor
//
@Override
public Visitor visitor(final Class klass) {
if (klass==PlainVanillaPayoff.class)
return (Visitor) plainVanillaPayoffVisitor;
else if (klass==CashOrNothingPayoff.class)
return (Visitor) cashOrNothingPayoffVisitor;
else if (klass==AssetOrNothingPayoff.class)
return (Visitor) assetOrNothingPayoffVisitor;
else if (klass==GapPayoff.class)
return (Visitor) gapPayoffVisitor;
else
throw new UnsupportedOperationException(INVALID_PAYOFF_TYPE + klass);
}
//
// implements Visitor
//
private final PlainVanillaPayoffVisitor plainVanillaPayoffVisitor = new PlainVanillaPayoffVisitor();
private static final class PlainVanillaPayoffVisitor implements Visitor {
@Override
public final void visit(final Payoff o) {
// nothing
}
}
//
// implements Visitor
//
private final CashOrNothingPayoffVisitor cashOrNothingPayoffVisitor = new CashOrNothingPayoffVisitor();
private final class CashOrNothingPayoffVisitor implements Visitor {
@Override
public final void visit(final Payoff o) {
final CashOrNothingPayoff payoff = (CashOrNothingPayoff)o;
black.alpha = black.dAlpha_dD1 = 0.0;
black.x = payoff.getCashPayoff();
black.dx_dStrike = 0.0;
final Option.Type optionType = payoff.optionType();
if (optionType == Option.Type.Call) {
black.beta = black.cum_d2;
black.dBeta_dD2 = black.n_d2;
} else if (optionType == Option.Type.Put) {
black.beta = 1.0 - black.cum_d2;
black.dBeta_dD2 = -black.n_d2;
} else
throw new IllegalArgumentException(INVALID_OPTION_TYPE);
}
}
//
// implements Visitor
//
private final AssetOrNothingPayoffVisitor assetOrNothingPayoffVisitor = new AssetOrNothingPayoffVisitor();
private final class AssetOrNothingPayoffVisitor implements Visitor {
@Override
public void visit(final Payoff o) {
final AssetOrNothingPayoff payoff = (AssetOrNothingPayoff)o;
black.beta = black.dBeta_dD2 = 0.0;
final Option.Type optionType = payoff.optionType();
if (optionType == Option.Type.Call) {
black.alpha = black.cum_d1;
black.dAlpha_dD1 = black.n_d1;
} else if (optionType == Option.Type.Put) {
black.alpha = 1.0 - black.cum_d1;
black.dAlpha_dD1 = -black.n_d1;
} else
throw new IllegalArgumentException(INVALID_OPTION_TYPE);
}
}
//
// implements Visitor
//
private final GapPayoffVisitor gapPayoffVisitor = new GapPayoffVisitor();
private final class GapPayoffVisitor implements Visitor {
@Override
public final void visit(final Payoff o) {
final GapPayoff payoff = (GapPayoff)o;
black.x = payoff.getSecondStrike();
black.dx_dStrike = 0.0;
}
}
}
}
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