/*
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
<jquant-devel@lists.sourceforge.net>. The license is also available online at
<http://www.jquantlib.org/index.php/LICENSE.TXT>.
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) 2004 Neil Firth
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
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
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.vanilla;
import org.jquantlib.QL;
import org.jquantlib.daycounters.DayCounter;
import org.jquantlib.exercise.AmericanExercise;
import org.jquantlib.exercise.Exercise;
import org.jquantlib.instruments.Option;
import org.jquantlib.instruments.StrikedTypePayoff;
import org.jquantlib.instruments.VanillaOption;
import org.jquantlib.lang.exceptions.LibraryException;
import org.jquantlib.math.distributions.CumulativeNormalDistribution;
import org.jquantlib.math.distributions.NormalDistribution;
import org.jquantlib.pricingengines.BlackCalculator;
import org.jquantlib.pricingengines.BlackFormula;
import org.jquantlib.processes.GeneralizedBlackScholesProcess;
/**
* An Approximate Formula for Pricing American Options, Journal of Derivatives Winter 1999, Ju, N.
* <p>
* Known issue, the case of zero interest rates causes a division by zero
*
* @author <Richard Gomes>
*/
public class JuQuadraticApproximationEngine extends VanillaOption.EngineImpl {
// TODO: refactor messages
private static final String NOT_AN_AMERICAN_OPTION = "not an American Option";
private static final String NON_AMERICAN_EXERCISE_GIVEN = "non-American exercise given";
private static final String PAYOFF_AT_EXPIRY_NOT_HANDLED = "payoff at expiry not handled";
private static final String NON_STRIKE_PAYOFF_GIVEN = "non-striked payoff given";
private static final String BLACK_SCHOLES_PROCESS_REQUIRED = "Black-Scholes process required";
private static final String UNKNOWN_OPTION_TYPE = "unknown Option type";
private static final String DIVIDING_BY_ZERO_INTEREST_RATE = "dividing by zero interst rate";
//
// private final fields
//
final private GeneralizedBlackScholesProcess process;
final private VanillaOption.ArgumentsImpl a;
final private VanillaOption.ResultsImpl r;
private final Option.GreeksImpl greeks;
private final Option.MoreGreeksImpl moreGreeks;
//
// public constructors
//
public JuQuadraticApproximationEngine(final GeneralizedBlackScholesProcess process) {
this.a = (VanillaOption.ArgumentsImpl)arguments;
this.r = (VanillaOption.ResultsImpl)results;
this.greeks = r.greeks();
this.moreGreeks = r.moreGreeks();
this.process = process;
this.process.addObserver(this);
}
//
// implements PricingEngine
//
@Override
public void calculate() {
QL.require(a.exercise.type()==Exercise.Type.American , NOT_AN_AMERICAN_OPTION); // QA:[RG]::verified
QL.require(a.exercise instanceof AmericanExercise , NON_AMERICAN_EXERCISE_GIVEN); // QA:[RG]::verified
final AmericanExercise ex = (AmericanExercise)a.exercise;
QL.require(!ex.payoffAtExpiry() , PAYOFF_AT_EXPIRY_NOT_HANDLED); // QA:[RG]::verified
QL.require(a.payoff instanceof StrikedTypePayoff , NON_STRIKE_PAYOFF_GIVEN); // QA:[RG]::verified
final StrikedTypePayoff payoff = (StrikedTypePayoff)a.payoff;
final double /* @Real */variance = process.blackVolatility().currentLink().blackVariance(ex.lastDate(), payoff.strike());
final double /* @DiscountFactor */dividendDiscount = process.dividendYield().currentLink().discount(ex.lastDate());
final double /* @DiscountFactor */riskFreeDiscount = process.riskFreeRate().currentLink().discount(ex.lastDate());
final double /* @Real */spot = process.stateVariable().currentLink().value();
QL.require(spot > 0.0, "negative or null underlying given"); // QA:[RG]::verified // TODO: message
final double /* @Real */forwardPrice = spot * dividendDiscount / riskFreeDiscount;
final BlackCalculator black = new BlackCalculator(payoff, forwardPrice, Math.sqrt(variance), riskFreeDiscount);
if (dividendDiscount>=1.0 && payoff.optionType()==Option.Type.Call) {
// early exercise never optimal
r.value = black.value();
greeks.delta = black.delta(spot);
moreGreeks.deltaForward = black.deltaForward();
moreGreeks.elasticity = black.elasticity(spot);
greeks.gamma = black.gamma(spot);
final DayCounter rfdc = process.riskFreeRate().currentLink().dayCounter();
final DayCounter divdc = process.dividendYield().currentLink().dayCounter();
final DayCounter voldc = process.blackVolatility().currentLink().dayCounter();
double /*@Time*/ t = rfdc.yearFraction(process.riskFreeRate().currentLink().referenceDate(), a.exercise.lastDate());
greeks.rho = black.rho(t);
t = divdc.yearFraction(process.dividendYield().currentLink().referenceDate(), a.exercise.lastDate());
greeks.dividendRho = black.dividendRho(t);
t = voldc.yearFraction(process.blackVolatility().currentLink().referenceDate(), a.exercise.lastDate());
greeks.vega = black.vega(t);
greeks.theta = black.theta(spot, t);
moreGreeks.thetaPerDay = black.thetaPerDay(spot, t);
moreGreeks.strikeSensitivity = black.strikeSensitivity();
moreGreeks.itmCashProbability = black.itmCashProbability();
} else {
// early exercise can be optimal
final CumulativeNormalDistribution cumNormalDist = new CumulativeNormalDistribution();
final NormalDistribution normalDist = new NormalDistribution();
final double /*@Real*/ tolerance = 1e-6;
final double /*@Real*/ Sk = BaroneAdesiWhaleyApproximationEngine.criticalPrice(payoff, riskFreeDiscount, dividendDiscount, variance, tolerance);
final double /*@Real*/ forwardSk = Sk * dividendDiscount / riskFreeDiscount;
final double /*@Real*/ alpha = -2.0*Math.log(riskFreeDiscount)/(variance);
final double /*@Real*/ beta = 2.0*Math.log(dividendDiscount/riskFreeDiscount)/
(variance);
final double /*@Real*/ h = 1 - riskFreeDiscount;
double /*@Real*/ phi;
switch (payoff.optionType()) {
case Call:
phi = 1;
break;
case Put:
phi = -1;
break;
default:
throw new LibraryException(UNKNOWN_OPTION_TYPE); // QA:[RG]::verified
}
// TODO: study how zero interest rate could be handled
QL.ensure(h != 0.0 , DIVIDING_BY_ZERO_INTEREST_RATE); // QA:[RG]::verified
final double /* @Real */temp_root = Math.sqrt((beta - 1) * (beta - 1) + (4 * alpha) / h);
final double /* @Real */lambda = (-(beta - 1) + phi * temp_root) / 2;
final double /* @Real */lambda_prime = -phi * alpha / (h * h * temp_root);
final double /* @Real */black_Sk = BlackFormula.blackFormula(payoff.optionType(), payoff.strike(), forwardSk, Math.sqrt(variance)) * riskFreeDiscount;
final double /* @Real */hA = phi * (Sk - payoff.strike()) - black_Sk;
final double /* @Real */d1_Sk = (Math.log(forwardSk / payoff.strike()) + 0.5 * variance) / Math.sqrt(variance);
final double /* @Real */d2_Sk = d1_Sk - Math.sqrt(variance);
final double /* @Real */part1 = forwardSk * normalDist.op(d1_Sk) / (alpha * Math.sqrt(variance));
final double /* @Real */part2 = -phi * forwardSk * cumNormalDist.op(phi * d1_Sk) * Math.log(dividendDiscount) / Math.log(riskFreeDiscount);
final double /* @Real */part3 = +phi * payoff.strike() * cumNormalDist.op(phi * d2_Sk);
final double /* @Real */V_E_h = part1 + part2 + part3;
final double /* @Real */b = (1 - h) * alpha * lambda_prime / (2 * (2 * lambda + beta - 1));
final double /* @Real */c = -((1 - h) * alpha / (2 * lambda + beta - 1)) * (V_E_h / (hA) + 1 / h + lambda_prime / (2 * lambda + beta - 1));
final double /* @Real */temp_spot_ratio = Math.log(spot / Sk);
final double /* @Real */chi = temp_spot_ratio * (b * temp_spot_ratio + c);
if (phi * (Sk - spot) > 0) {
r.value = black.value() + hA * Math.pow((spot / Sk), lambda) / (1 - chi);
} else {
r.value = phi * (spot - payoff.strike());
}
final double /* @Real */temp_chi_prime = (2 * b / spot) * Math.log(spot / Sk);
final double /* @Real */chi_prime = temp_chi_prime + c / spot;
final double /* @Real */chi_double_prime = 2 * b / (spot * spot) - temp_chi_prime / spot - c / (spot * spot);
greeks.delta = phi * dividendDiscount * cumNormalDist.op(phi * d1_Sk)
+ (lambda / (spot * (1 - chi)) + chi_prime / ((1 - chi)*(1 - chi))) *
(phi * (Sk - payoff.strike()) - black_Sk) * Math.pow((spot/Sk), lambda);
greeks.gamma = phi * dividendDiscount * normalDist.op(phi*d1_Sk) /
(spot * Math.sqrt(variance))
+ (2 * lambda * chi_prime / (spot * (1 - chi) * (1 - chi))
+ 2 * chi_prime * chi_prime / ((1 - chi) * (1 - chi) * (1 - chi))
+ chi_double_prime / ((1 - chi) * (1 - chi))
+ lambda * (1 - lambda) / (spot * spot * (1 - chi)))
* (phi * (Sk - payoff.strike()) - black_Sk)
* Math.pow((spot/Sk), lambda);
}
} // end of "early exercise can be optimal"
}