/*
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 Ferdinando Ametrano
Copyright (C) 2005 StatPro Italia srl
Copyright (C) 2005 Joseph Wang
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.
*/
/**
*
* Ported from
*
* - test-suite/americanoption.cpp
*
*
* @author
*
*/
package org.jquantlib.testsuite.instruments;
import static org.junit.Assert.fail;
import java.lang.reflect.Constructor;
import java.util.HashMap;
import java.util.Map;
import java.util.Map.Entry;
import org.jquantlib.QL;
import org.jquantlib.Settings;
import org.jquantlib.daycounters.Actual360;
import org.jquantlib.daycounters.DayCounter;
import org.jquantlib.exercise.AmericanExercise;
import org.jquantlib.exercise.Exercise;
import org.jquantlib.instruments.Option;
import org.jquantlib.instruments.PlainVanillaPayoff;
import org.jquantlib.instruments.StrikedTypePayoff;
import org.jquantlib.instruments.VanillaOption;
import org.jquantlib.instruments.Option.Type;
import org.jquantlib.pricingengines.PricingEngine;
import org.jquantlib.pricingengines.vanilla.BaroneAdesiWhaleyApproximationEngine;
import org.jquantlib.pricingengines.vanilla.BjerksundStenslandApproximationEngine;
import org.jquantlib.pricingengines.vanilla.JuQuadraticApproximationEngine;
import org.jquantlib.pricingengines.vanilla.finitedifferences.FDAmericanEngine;
import org.jquantlib.pricingengines.vanilla.finitedifferences.FDShoutEngine;
import org.jquantlib.processes.BlackScholesMertonProcess;
import org.jquantlib.processes.GeneralizedBlackScholesProcess;
import org.jquantlib.quotes.Handle;
import org.jquantlib.quotes.Quote;
import org.jquantlib.quotes.SimpleQuote;
import org.jquantlib.termstructures.BlackVolTermStructure;
import org.jquantlib.termstructures.YieldTermStructure;
import org.jquantlib.testsuite.util.Utilities;
import org.jquantlib.time.Date;
import org.jquantlib.time.Period;
import org.jquantlib.time.TimeUnit;
import org.junit.Test;
public class AmericanOptionTest {
public AmericanOptionTest() {
QL.info("::::: " + this.getClass().getSimpleName() + " :::::");
}
@Test
public void testBjerksundStenslandValues() {
QL.info("Testing Bjerksund and Stensland approximation for American options...");
// type, strike, spot, q, r, t, vol, value, tol
final AmericanOptionData values[] = {
// From "Option pricing formulas", Haug, McGraw-Hill 1998, pag 27
new AmericanOptionData(Option.Type.Call, 40.00, 42.00, 0.08, 0.04, 0.75, 0.35, 5.2704),
// From "Option pricing formulas", Haug, McGraw-Hill 1998, VBA
new AmericanOptionData(Option.Type.Put, 40.00, 36.00, 0.00, 0.06, 1.00, 0.20, 4.4531) };
final Date today = new Settings().evaluationDate();
final DayCounter dc = new Actual360();
final SimpleQuote spot = new SimpleQuote(0.0);
final SimpleQuote qRate = new SimpleQuote(0.0);
final YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
final SimpleQuote rRate = new SimpleQuote(0.0);
final YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
final SimpleQuote vol = new SimpleQuote(0.0);
final BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
final double /* @Real */tolerance = 1.0e-4;
for (final AmericanOptionData value : values) {
final StrikedTypePayoff payoff = new PlainVanillaPayoff(value.type, value.strike);
final int daysToExpiry = (int) (value.t * 360 + 0.5);
final Date exDate = today.clone().addAssign(daysToExpiry);
final Exercise exercise = new AmericanExercise(today, exDate);
spot.setValue(value.s);
qRate.setValue(value.q);
rRate.setValue(value.r);
vol.setValue(value.v);
final BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(
new Handle(spot),
new Handle(qTS),
new Handle(rTS),
new Handle(volTS));
final PricingEngine engine = new BjerksundStenslandApproximationEngine(stochProcess);
final VanillaOption option = new VanillaOption(payoff, exercise);
option.setPricingEngine(engine);
final double /* @Real */calculated = option.NPV();
final double /* @Real */error = Math.abs(calculated - value.result);
if (error > tolerance) {
reportFailure(
"value", payoff, exercise,
value.s, value.q, value.r, today, value.v,
value.result, calculated, error, tolerance);
}
}
}
@Test
public void testBaroneAdesiWhaley() {
QL.info("Testing Barone-Adesi and Whaley approximation for American options...");
/**
* The data below are from "Option pricing formulas", E.G. Haug, McGraw-Hill 1998 pag 24
*
* The following values were replicated only up to the second digit by the VB code provided by Haug, which was used as base
* for the C++ implementation
*/
final AmericanOptionData values[] = {
// type, strike, spot, q, r, t, vol, value
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.15, 0.0206),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.15, 1.8771),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.15, 10.0089),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.25, 0.3159),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.25, 3.1280),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.25, 10.3919),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.35, 0.9495),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.35, 4.3777),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.35, 11.1679),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.15, 0.8208),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.15, 4.0842),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.15, 10.8087),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.25, 2.7437),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.25, 6.8015),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.25, 13.0170),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.35, 5.0063),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.35, 9.5106),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.35, 15.5689),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.15, 10.0000),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.15, 1.8770),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.15, 0.0410),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.25, 10.2533),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.25, 3.1277),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.25, 0.4562),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.35, 10.8787),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.35, 4.3777),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.35, 1.2402),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.15, 10.5595),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.15, 4.0842),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.15, 1.0822),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.25, 12.4419),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.25, 6.8014),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.25, 3.3226),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.35, 14.6945),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.35, 9.5104),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.35, 5.8823) };
final Date today = new Settings().evaluationDate();
final DayCounter dc = new Actual360();
final SimpleQuote spot = new SimpleQuote(0.0);
final SimpleQuote qRate = new SimpleQuote(0.0);
final YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
final SimpleQuote rRate = new SimpleQuote(0.0);
final YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
final SimpleQuote vol = new SimpleQuote(0.0);
final BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
final double /* @Real */tolerance = 3.0e-3;
for (final AmericanOptionData value : values) {
final StrikedTypePayoff payoff = new PlainVanillaPayoff(value.type, value.strike);
final Date exDate = today.add(timeToDays(value.t));
final Exercise exercise = new AmericanExercise(today, exDate);
spot.setValue(value.s);
qRate.setValue(value.q);
rRate.setValue(value.r);
vol.setValue(value.v);
final BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(
new Handle(spot),
new Handle(qTS),
new Handle(rTS),
new Handle(volTS));
final PricingEngine engine = new BaroneAdesiWhaleyApproximationEngine(stochProcess);
final VanillaOption option = new VanillaOption(payoff, exercise);
option.setPricingEngine(engine);
final double /* @Real */calculated = option.NPV();
final double /* @Real */error = Math.abs(calculated - value.result);
if (error > tolerance) {
reportFailure(
"value", payoff, exercise,
value.s, value.q, value.r, today, value.v,
value.result, calculated, error, tolerance);
}
}
}
@Test
public void testJu() {
/*
* The data below are from An Approximate Formula for Pricing American Options Journal of Derivatives Winter 1999 Ju, N.
*/
final AmericanOptionData juValues[] = {
// type, strike, spot, q, r, t, vol, value, tol
// These values are from Exhibit 3 - Short dated Put Options
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.0833, 0.2, 0.006),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.3333, 0.2, 0.201),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.5833, 0.2, 0.433),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.0833, 0.2, 0.851),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.3333, 0.2, 1.576),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.5833, 0.2, 1.984),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.0833, 0.2, 5.000),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.3333, 0.2, 5.084),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.5833, 0.2, 5.260),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.0833, 0.3, 0.078),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.3333, 0.3, 0.697),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.5833, 0.3, 1.218),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.0833, 0.3, 1.309),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.3333, 0.3, 2.477),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.5833, 0.3, 3.161),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.0833, 0.3, 5.059),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.3333, 0.3, 5.699),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.5833, 0.3, 6.231),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.0833, 0.4, 0.247),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.3333, 0.4, 1.344),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.5833, 0.4, 2.150),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.0833, 0.4, 1.767),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.3333, 0.4, 3.381),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.5833, 0.4, 4.342),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.0833, 0.4, 5.288),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.3333, 0.4, 6.501),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.5833, 0.4, 7.367),
// Type in Exhibits 4 and 5 if you have some spare time ;-)
// type, strike, spot, q, r, t, vol, value, tol
// These values are from Exhibit 6 - Long dated Call Options
// with dividends
new AmericanOptionData(Option.Type.Call, 100.00, 80.00, 0.07, 0.03, 3.0, 0.2, 2.605),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.07, 0.03, 3.0, 0.2, 5.182),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.07, 0.03, 3.0, 0.2, 9.065),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.07, 0.03, 3.0, 0.2, 14.430),
new AmericanOptionData(Option.Type.Call, 100.00, 120.00, 0.07, 0.03, 3.0, 0.2, 21.398),
new AmericanOptionData(Option.Type.Call, 100.00, 80.00, 0.07, 0.03, 3.0, 0.4, 11.336),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.07, 0.03, 3.0, 0.4, 15.711),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.07, 0.03, 3.0, 0.4, 20.760),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.07, 0.03, 3.0, 0.4, 26.440),
new AmericanOptionData(Option.Type.Call, 100.00, 120.00, 0.07, 0.03, 3.0, 0.4, 32.709),
// FIXME case of zero interest rates not handled
// new AmericanOptionData(Option.Type.CALL, 100.00, 80.00, 0.07, 0.0, 3.0, 0.3, 5.552 ),
// new AmericanOptionData(Option.Type.CALL, 100.00, 90.00, 0.07, 0.0, 3.0, 0.3, 8.868 ),
// new AmericanOptionData(Option.Type.CALL, 100.00, 100.00, 0.07, 0.0, 3.0, 0.3, 13.158 ),
// new AmericanOptionData(Option.Type.CALL, 100.00, 110.00, 0.07, 0.0, 3.0, 0.3, 18.458 ),
// new AmericanOptionData(Option.Type.CALL, 100.00, 120.00, 0.07, 0.0, 3.0, 0.3, 24.786 ),
new AmericanOptionData(Option.Type.Call, 100.00, 80.00, 0.03, 0.07, 3.0, 0.3, 12.177),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.03, 0.07, 3.0, 0.3, 17.411),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.03, 0.07, 3.0, 0.3, 23.402),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.03, 0.07, 3.0, 0.3, 30.028),
new AmericanOptionData(Option.Type.Call, 100.00, 120.00, 0.03, 0.07, 3.0, 0.3, 37.177) };
QL.info("Testing Ju approximation for American options...");
final Date today = new Settings().evaluationDate();
final DayCounter dc = new Actual360();
final SimpleQuote spot = new SimpleQuote(0.0);
final SimpleQuote qRate = new SimpleQuote(0.0);
final YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
final SimpleQuote rRate = new SimpleQuote(0.0);
final YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
final SimpleQuote vol = new SimpleQuote(0.0);
final BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
final double tolerance = 1.0e-3;
for (final AmericanOptionData juValue : juValues) {
final StrikedTypePayoff payoff = new PlainVanillaPayoff(juValue.type, juValue.strike);
final Date exDate = today.add(timeToDays(juValue.t));
final Exercise exercise = new AmericanExercise(today, exDate);
spot.setValue(juValue.s);
qRate.setValue(juValue.q);
rRate.setValue(juValue.r);
vol.setValue(juValue.v);
final BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(
new Handle(spot),
new Handle(qTS),
new Handle(rTS),
new Handle(volTS));
final PricingEngine engine = new JuQuadraticApproximationEngine(stochProcess);
final VanillaOption option = new VanillaOption(payoff, exercise);
option.setPricingEngine(engine);
final double calculated = option.NPV();
final double error = Math.abs(calculated - juValue.result);
if (error > tolerance) {
reportFailure(
"value", payoff, exercise,
juValue.s, juValue.q, juValue.r, today, juValue.v,
juValue.result, calculated, error, tolerance);
}
}
}
@Test
public void testFdValues() {
QL.info("Testing finite-difference engine for American options...");
/**
* The data below are from An Approximate Formula for Pricing American Options Journal of Derivatives Winter 1999 Ju, N.
*/
final AmericanOptionData juValues[] = {
// type, strike, spot, q, r, t, vol, value, tol
// These values are from Exhibit 3 - Short dated Put Options
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.0833, 0.2, 0.006),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.3333, 0.2, 0.201),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.5833, 0.2, 0.433),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.0833, 0.2, 0.851),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.3333, 0.2, 1.576),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.5833, 0.2, 1.984),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.0833, 0.2, 5.000),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.3333, 0.2, 5.084),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.5833, 0.2, 5.260),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.0833, 0.3, 0.078),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.3333, 0.3, 0.697),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.5833, 0.3, 1.218),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.0833, 0.3, 1.309),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.3333, 0.3, 2.477),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.5833, 0.3, 3.161),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.0833, 0.3, 5.059),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.3333, 0.3, 5.699),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.5833, 0.3, 6.231),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.0833, 0.4, 0.247),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.3333, 0.4, 1.344),
new AmericanOptionData(Option.Type.Put, 35.00, 40.00, 0.0, 0.0488, 0.5833, 0.4, 2.150),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.0833, 0.4, 1.767),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.3333, 0.4, 3.381),
new AmericanOptionData(Option.Type.Put, 40.00, 40.00, 0.0, 0.0488, 0.5833, 0.4, 4.342),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.0833, 0.4, 5.288),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.3333, 0.4, 6.501),
new AmericanOptionData(Option.Type.Put, 45.00, 40.00, 0.0, 0.0488, 0.5833, 0.4, 7.367),
// Type in Exhibits 4 and 5 if you have some spare time ;-)
// type, strike, spot, q, r, t, vol, value, tol
// These values are from Exhibit 6 - Long dated Call Options
// with dividends
new AmericanOptionData(Option.Type.Call, 100.00, 80.00, 0.07, 0.03, 3.0, 0.2, 2.605),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.07, 0.03, 3.0, 0.2, 5.182),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.07, 0.03, 3.0, 0.2, 9.065),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.07, 0.03, 3.0, 0.2, 14.430),
new AmericanOptionData(Option.Type.Call, 100.00, 120.00, 0.07, 0.03, 3.0, 0.2, 21.398),
new AmericanOptionData(Option.Type.Call, 100.00, 80.00, 0.07, 0.03, 3.0, 0.4, 11.336),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.07, 0.03, 3.0, 0.4, 15.711),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.07, 0.03, 3.0, 0.4, 20.760),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.07, 0.03, 3.0, 0.4, 26.440),
new AmericanOptionData(Option.Type.Call, 100.00, 120.00, 0.07, 0.03, 3.0, 0.4, 32.709),
// FIXME case of zero interest rates not handled
// new AmericanOptionData(Option.Type.CALL, 100.00, 80.00, 0.07, 0.0, 3.0, 0.3, 5.552 ),
// new AmericanOptionData(Option.Type.CALL, 100.00, 90.00, 0.07, 0.0, 3.0, 0.3, 8.868 ),
// new AmericanOptionData(Option.Type.CALL, 100.00, 100.00, 0.07, 0.0, 3.0, 0.3, 13.158 ),
// new AmericanOptionData(Option.Type.CALL, 100.00, 110.00, 0.07, 0.0, 3.0, 0.3, 18.458 ),
// new AmericanOptionData(Option.Type.CALL, 100.00, 120.00, 0.07, 0.0, 3.0, 0.3, 24.786 ),
new AmericanOptionData(Option.Type.Call, 100.00, 80.00, 0.03, 0.07, 3.0, 0.3, 12.177),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.03, 0.07, 3.0, 0.3, 17.411),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.03, 0.07, 3.0, 0.3, 23.402),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.03, 0.07, 3.0, 0.3, 30.028),
new AmericanOptionData(Option.Type.Call, 100.00, 120.00, 0.03, 0.07, 3.0, 0.3, 37.177) };
final Date today = new Settings().evaluationDate();
final double tolerance = 8.0e-2;
for (final AmericanOptionData juValue : juValues) {
final DayCounter dc = new Actual360();
final SimpleQuote spot = new SimpleQuote(0.0);
final SimpleQuote qRate = new SimpleQuote(0.0);
final YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
final SimpleQuote rRate = new SimpleQuote(0.0);
final YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
final SimpleQuote vol = new SimpleQuote(0.0);
final BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
final StrikedTypePayoff payoff = new PlainVanillaPayoff(juValue.type, juValue.strike);
final Date exDate = today.add(timeToDays(juValue.t));
final Exercise exercise = new AmericanExercise(today, exDate);
spot.setValue(juValue.s);
qRate.setValue(juValue.q);
rRate.setValue(juValue.r);
vol.setValue(juValue.v);
final BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(
new Handle(spot),
new Handle(qTS),
new Handle(rTS),
new Handle(volTS));
final PricingEngine engine = new FDAmericanEngine(stochProcess, 100, 100);
final VanillaOption option = new VanillaOption(payoff, exercise);
option.setPricingEngine(engine);
final double calculated = option.NPV();
final double error = Math.abs(calculated - juValue.result);
if (error > tolerance) {
reportFailure(
"value", payoff, exercise,
juValue.s, juValue.q, juValue.r, today, juValue.v,
juValue.result, calculated, error, tolerance);
}
}
}
@Test
public void testFdAmericanGreeks() {
QL.info("Testing Greeks (delta, gamma, theta for American options using FDAmericanEngine");
testFdGreeks(FDAmericanEngine.class);
}
@Test
public void testFdShoutGreeks() {
QL.info("Testing Greeks (delta, gamma, theta for American options using FDShoutEngine");
testFdGreeks(FDShoutEngine.class);
}
private void testFdGreeks(final Class klass) {
final Map calculated = new HashMap();
final Map expected = new HashMap();
final Map tolerance = new HashMap();
tolerance.put("delta", 7.0e-4);
tolerance.put("gamma", 2.0e-4);
tolerance.put("theta", 1.0e-4);
final Option.Type types[] = { Option.Type.Call, Option.Type.Put };
final double strikes[] = { 50.0, 99.5, 100.0, 100.5, 150.0 };
final double underlyings[] = { 100.0 };
final double qRates[] = { 0.04, 0.05, 0.06 };
final double rRates[] = { 0.01, 0.05, 0.15 };
final int years[] = { 1, 2 };
final double vols[] = { 0.11, 0.50, 1.20 };
final DayCounter dc = new Actual360();
final Date today = new Settings().evaluationDate();
final SimpleQuote spot = new SimpleQuote(0.0);
final SimpleQuote qRate = new SimpleQuote(0.0);
final YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
final SimpleQuote rRate = new SimpleQuote(0.0);
final YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
final SimpleQuote vol = new SimpleQuote(0.0);
final BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
for (final Type type : types) {
for (final double strike : strikes) {
for (final int year : years) {
final Date exDate = today.add(new Period(year, TimeUnit.Years));
final Exercise exercise = new AmericanExercise(today, exDate);
final StrikedTypePayoff payoff = new PlainVanillaPayoff(type, strike);
final BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(
new Handle(spot),
new Handle(qTS),
new Handle(rTS),
new Handle(volTS));
PricingEngine engine = null;
try {
final Constructor c = klass.getConstructor(GeneralizedBlackScholesProcess.class);
engine = c.newInstance(stochProcess);
} catch (final Exception e) {
e.printStackTrace();
fail("failed to create pricing engine");
}
final VanillaOption option = new VanillaOption(payoff, exercise);
option.setPricingEngine(engine);
for (final double u : underlyings) {
for (final double q : qRates) {
for (final double r : rRates) {
for (final double v : vols) {
spot.setValue(u);
qRate.setValue(q);
rRate.setValue(r);
vol.setValue(v);
// FLOATING_POINT_EXCEPTION
final double value = option.NPV();
final double delta = option.delta();
final double gamma = option.gamma();
//final double theta = option.theta();
calculated.put("delta", delta);
calculated.put("gamma", gamma);
//calculated.put("theta", theta);
if (value > spot.value() * 1.0e-5) {
// perturb spot and get delta and gamma
final double du = u * 1.0e-4;
spot.setValue(u + du);
final double value_p = option.NPV();
final double delta_p = option.delta();
spot.setValue(u - du);
final double value_m = option.NPV();
final double delta_m = option.delta();
spot.setValue(u);
expected.put("delta", (value_p - value_m) / (2 * du));
expected.put("gamma", (delta_p - delta_m) / (2 * du));
/*
// perturb date and get theta
final Date yesterday = today.sub(1);
final Date tomorrow = today.add(1);
final double dT = dc.yearFraction(yesterday, tomorrow);
new Settings().setEvaluationDate(yesterday);
value_m = option.getNPV();
new Settings().setEvaluationDate(tomorrow);
value_p = option.getNPV();
expected.put("theta", (value_p - value_m) / dT);
*/
// compare
for (final Entry greek : calculated.entrySet()) {
final double expct = expected.get(greek.getKey());
final double calcl = calculated.get(greek.getKey());
final double tol = tolerance.get(greek.getKey());
final double error = Utilities.relativeError(expct, calcl, u);
if (error > tol) {
reportFailure(
greek.getKey(), payoff, exercise,
u, q, r, today, v,
expct, calcl, error, tol);
}
}
}
}
}
}
}
}
}
}
}
private void reportFailure(
final String greekName,
final StrikedTypePayoff payoff,
final Exercise exercise,
final double s,
final double q,
final double r,
final Date today,
final double v,
final double expected,
final double calculated,
final double error,
final double tolerance) {
final StringBuilder sb = new StringBuilder();
sb.append(exercise.type()).append(' ');
sb.append(payoff.optionType()).append(" option with ").append(payoff.getClass().getSimpleName()).append(" payoff:\n");
sb.append(" spot value: ").append(s).append('\n');
sb.append(" strike: ").append(payoff.strike()).append('\n');
sb.append(" dividend yield: ").append(q).append('\n');
sb.append(" risk-free rate: ").append(r).append('\n');
sb.append(" reference date: ").append(today).append('\n');
sb.append(" maturity: ").append(exercise.lastDate()).append('\n');
sb.append(" volatility: ").append(v).append('\n');
sb.append(" expected ").append(greekName).append(": ").append(expected).append('\n');
sb.append(" calculated ").append(greekName).append(": ").append(calculated).append('\n');
sb.append(" error: ").append(error).append('\n');
sb.append(" tolerance: ").append(tolerance).append('\n');
fail(sb.toString());
}
private int timeToDays(/* @Time */final double t) {
return (int) (t * 360 + 0.5);
}
//
// private inner classes
//
private class AmericanOptionData {
private final Option.Type type;
private final double /* @Real */strike;
private final double /* @Real */s; // spot
private final double /* @Rate */q; // dividend
private final double /* @Rate */r; // risk-free rate
private final double /* @Time */t; // time to maturity
private final double /* @Volatility */v; // volatility
private final double /* @Real */result; // expected result
public AmericanOptionData(
final Option.Type type,
final double strike,
final double s,
final double q,
final double r,
final double t,
final double v,
final double result) {
this.type = type;
this.strike = strike;
this.s = s;
this.q = q;
this.r = r;
this.t = t;
this.v = v;
this.result = result;
}
@Override
public String toString() {
final StringBuilder builder = new StringBuilder();
builder.append("Type: " + type);
builder.append(" Strike: " + strike);
builder.append(" Spot: " + s);
builder.append(" DividendYield: " + q);
builder.append(" Riskfree: " + r);
builder.append(" TTm: " + t);
builder.append(" Vol: " + v);
builder.append(" result: " + result);
return builder.toString();
}
}
}
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