/**
* Copyright (C) 2013 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.model.option.pricing.tree;
import static org.testng.Assert.assertEquals;
import static org.testng.AssertJUnit.assertFalse;
import static org.testng.AssertJUnit.assertTrue;
import org.testng.annotations.Test;
import com.opengamma.analytics.financial.greeks.Greek;
import com.opengamma.analytics.financial.greeks.GreekResultCollection;
import com.opengamma.analytics.math.statistics.distribution.NormalDistribution;
import com.opengamma.analytics.math.statistics.distribution.ProbabilityDistribution;
/**
*
*/
public class AssetOrNothingOptionFunctionProviderTest {
private static final ProbabilityDistribution<Double> NORMAL = new NormalDistribution(0, 1);
private static final BinomialTreeOptionPricingModel _model = new BinomialTreeOptionPricingModel();
private static final TrinomialTreeOptionPricingModel _modelTrinomial = new TrinomialTreeOptionPricingModel();
private static final double SPOT = 105.;
private static final double[] STRIKES = new double[] {97., 105., 105.1, 114. };
private static final double TIME = 4.2;
private static final double[] INTERESTS = new double[] {-0.01, 0., 0.017, 0.05 };
private static final double[] VOLS = new double[] {0.05, 0.1, 0.5 };
private static final double[] DIVIDENDS = new double[] {0., 0.005, 0.014 };
/**
*
*/
@Test
public void priceLatticeTrinomialTest() {
final LatticeSpecification[] lattices = new LatticeSpecification[] {new CoxRossRubinsteinLatticeSpecification(), new JarrowRuddLatticeSpecification(),
new TrigeorgisLatticeSpecification(), new TianLatticeSpecification() };
final boolean[] tfSet = new boolean[] {true, false };
for (final LatticeSpecification lattice : lattices) {
for (final boolean isCall : tfSet) {
for (final double strike : STRIKES) {
for (final double interest : INTERESTS) {
for (final double vol : VOLS) {
final int nSteps = 451;
for (final double dividend : DIVIDENDS) {
final OptionFunctionProvider1D function = new AssetOrNothingOptionFunctionProvider(strike, TIME, nSteps, isCall);
final double exactDiv = price(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double resDiv = _modelTrinomial.getPrice(lattice, function, SPOT, vol, interest, dividend);
final double refDiv = Math.max(exactDiv, .1) * 1.e-1;
assertEquals(resDiv, exactDiv, refDiv);
}
}
}
}
}
}
}
/**
*
*/
@Test
public void greekTrinomialTest() {
final LatticeSpecification lattice = new TianLatticeSpecification();
final boolean[] tfSet = new boolean[] {true, false };
for (final boolean isCall : tfSet) {
for (final double strike : STRIKES) {
for (final double interest : INTERESTS) {
for (final double vol : VOLS) {
final int nSteps = 1059;
for (final double dividend : DIVIDENDS) {
final OptionFunctionProvider1D function = new AssetOrNothingOptionFunctionProvider(strike, TIME, nSteps, isCall);
final GreekResultCollection resDiv = _modelTrinomial.getGreeks(lattice, function, SPOT, vol, interest, dividend);
final double priceDiv = price(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refPriceDiv = Math.max(Math.abs(priceDiv), 1.) * 1.e-1;
assertEquals(resDiv.get(Greek.FAIR_PRICE), priceDiv, refPriceDiv);
final double deltaDiv = delta(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refDeltaDiv = Math.max(Math.abs(deltaDiv), 1.) * 1.e-1;
assertEquals(resDiv.get(Greek.DELTA), deltaDiv, refDeltaDiv);
final double gammaDiv = gamma(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refGammaDiv = Math.max(Math.abs(gammaDiv), 1.) * 1.e-1;
assertEquals(resDiv.get(Greek.GAMMA), gammaDiv, refGammaDiv);
final double thetaDiv = theta(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refThetaDiv = Math.max(Math.abs(thetaDiv), 1.) * 1.e-1;
assertEquals(resDiv.get(Greek.THETA), thetaDiv, refThetaDiv);
}
}
}
}
}
}
/**
*
*/
@Test
public void priceLatticeTest() {
final LatticeSpecification[] lattices = new LatticeSpecification[] {new CoxRossRubinsteinLatticeSpecification(), new JarrowRuddLatticeSpecification(), new TrigeorgisLatticeSpecification(),
new JabbourKraminYoungLatticeSpecification(), new TianLatticeSpecification() };
final boolean[] tfSet = new boolean[] {true, false };
for (final LatticeSpecification lattice : lattices) {
for (final boolean isCall : tfSet) {
for (final double strike : STRIKES) {
for (final double interest : INTERESTS) {
for (final double vol : VOLS) {
final int nSteps = 631;
for (final double dividend : DIVIDENDS) {
final OptionFunctionProvider1D function = new AssetOrNothingOptionFunctionProvider(strike, TIME, nSteps, isCall);
final double exactDiv = price(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double resDiv = _model.getPrice(lattice, function, SPOT, vol, interest, dividend);
final double refDiv = Math.max(exactDiv, 1.) * 1.e-1;
assertEquals(resDiv, exactDiv, refDiv);
}
}
}
}
}
}
}
/**
*
*/
@Test
public void priceeisenReimerTest() {
final LatticeSpecification lattice = new LeisenReimerLatticeSpecification();
final boolean[] tfSet = new boolean[] {true, false };
for (final boolean isCall : tfSet) {
for (final double strike : STRIKES) {
for (final double interest : INTERESTS) {
for (final double vol : VOLS) {
final int nSteps = 631;
for (final double dividend : DIVIDENDS) {
final OptionFunctionProvider1D function = new AssetOrNothingOptionFunctionProvider(strike, TIME, nSteps, isCall);
final double exactDiv = price(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double resDiv = _model.getPrice(lattice, function, SPOT, vol, interest, dividend);
final double refDiv = Math.max(exactDiv, 1.) * 1.e-6;
assertEquals(resDiv, exactDiv, refDiv);
}
}
}
}
}
}
/**
* The dividend is cash or proportional to asset price
*/
@Test
public void priceDiscreteDividendTest() {
final LatticeSpecification[] lattices = new LatticeSpecification[] {new CoxRossRubinsteinLatticeSpecification(), new JarrowRuddLatticeSpecification(), new TrigeorgisLatticeSpecification(),
new JabbourKraminYoungLatticeSpecification(), new TianLatticeSpecification(), new LeisenReimerLatticeSpecification() };
final double[] propDividends = new double[] {0.01, 0.01, 0.01 };
final double[] cashDividends = new double[] {5., 10., 8. };
final double[] dividendTimes = new double[] {TIME / 6., TIME / 3., TIME / 2. };
final boolean[] tfSet = new boolean[] {true, false };
for (final LatticeSpecification lattice : lattices) {
for (final boolean isCall : tfSet) {
for (final double strike : STRIKES) {
for (final double interest : INTERESTS) {
for (final double vol : VOLS) {
final int nSteps = 631;
final int nStepsTri = 231;
final OptionFunctionProvider1D function = new AssetOrNothingOptionFunctionProvider(strike, TIME, nSteps, isCall);
final DividendFunctionProvider cashDividend = new CashDividendFunctionProvider(dividendTimes, cashDividends);
final DividendFunctionProvider propDividend = new ProportionalDividendFunctionProvider(dividendTimes, propDividends);
final double resSpot = SPOT * (1. - propDividends[0]) * (1. - propDividends[1]) * (1. - propDividends[2]);
final double modSpot = SPOT - cashDividends[0] * Math.exp(-interest * dividendTimes[0]) - cashDividends[1] * Math.exp(-interest * dividendTimes[1]) - cashDividends[2] *
Math.exp(-interest * dividendTimes[2]);
final double exactProp = price(resSpot, strike, TIME, vol, interest, interest, isCall);
final double appCash = price(modSpot, strike, TIME, vol, interest, interest, isCall);
final double resProp = _model.getPrice(lattice, function, SPOT, vol, interest, propDividend);
final double refProp = Math.max(exactProp, 1.) * 1.e-1;
assertEquals(resProp, exactProp, refProp);
final double resCash = _model.getPrice(lattice, function, SPOT, vol, interest, cashDividend);
final double refCash = Math.max(appCash, 1.) * 1.e-1;
assertEquals(resCash, appCash, refCash);
if (lattice instanceof CoxRossRubinsteinLatticeSpecification || lattice instanceof JarrowRuddLatticeSpecification || lattice instanceof TrigeorgisLatticeSpecification ||
lattice instanceof TianLatticeSpecification) {
final OptionFunctionProvider1D functionTri = new AssetOrNothingOptionFunctionProvider(strike, TIME, nStepsTri, isCall);
final double resPropTrinomial = _modelTrinomial.getPrice(lattice, functionTri, SPOT, vol, interest, propDividend);
final double resCashTrinomial = _modelTrinomial.getPrice(lattice, functionTri, SPOT, vol, interest, cashDividend);
assertEquals(resPropTrinomial, exactProp, Math.max(exactProp, 1.) * 1.e-1);
assertEquals(resCashTrinomial, appCash, Math.max(appCash, 1.) * 1.e-1);
}
}
}
}
}
}
}
/**
* Due to a problem of computation time, only LeisenReimerLatticeSpecification in the next test is kept switched on
*/
@Test(enabled = false)
public void greekTest() {
final LatticeSpecification[] lattices = new LatticeSpecification[] {new CoxRossRubinsteinLatticeSpecification(), new JarrowRuddLatticeSpecification(),
new TrigeorgisLatticeSpecification(), new JabbourKraminYoungLatticeSpecification(), new TianLatticeSpecification() };
final boolean[] tfSet = new boolean[] {true, false };
for (final LatticeSpecification lattice : lattices) {
for (final boolean isCall : tfSet) {
for (final double strike : STRIKES) {
for (final double interest : INTERESTS) {
for (final double vol : VOLS) {
final int nSteps = 3037; //Slow convergence
for (final double dividend : DIVIDENDS) {
final OptionFunctionProvider1D function = new AssetOrNothingOptionFunctionProvider(strike, TIME, nSteps, isCall);
final GreekResultCollection resDiv = _model.getGreeks(lattice, function, SPOT, vol, interest, dividend);
final double priceDiv = price(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refPriceDiv = Math.max(Math.abs(priceDiv), 1.) * 1.e-1;
assertEquals(resDiv.get(Greek.FAIR_PRICE), priceDiv, refPriceDiv);
final double deltaDiv = delta(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refDeltaDiv = Math.max(Math.abs(deltaDiv), 1.) * 1.e-1;
assertEquals(resDiv.get(Greek.DELTA), deltaDiv, refDeltaDiv);
final double gammaDiv = gamma(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refGammaDiv = Math.max(Math.abs(gammaDiv), 1.) * 1.e-1;
assertEquals(resDiv.get(Greek.GAMMA), gammaDiv, refGammaDiv);
final double thetaDiv = theta(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refThetaDiv = Math.max(Math.abs(thetaDiv), 1.) * 1.e-1;
assertEquals(resDiv.get(Greek.THETA), thetaDiv, refThetaDiv);
}
}
}
}
}
}
}
/**
*
*/
@Test
public void greekLeisenReimerTest() {
final LatticeSpecification lattice = new LeisenReimerLatticeSpecification();
final boolean[] tfSet = new boolean[] {true, false };
for (final boolean isCall : tfSet) {
for (final double strike : STRIKES) {
for (final double interest : INTERESTS) {
for (final double vol : VOLS) {
final int nSteps = 631;
for (final double dividend : DIVIDENDS) {
final OptionFunctionProvider1D function = new AssetOrNothingOptionFunctionProvider(strike, TIME, nSteps, isCall);
final GreekResultCollection resDiv = _model.getGreeks(lattice, function, SPOT, vol, interest, dividend);
final double priceDiv = price(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refPriceDiv = Math.max(Math.abs(priceDiv), 1.) * 1.e-6;
assertEquals(resDiv.get(Greek.FAIR_PRICE), priceDiv, refPriceDiv);
final double deltaDiv = delta(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refDeltaDiv = Math.max(Math.abs(deltaDiv), 1.) * 1.e-2;
assertEquals(resDiv.get(Greek.DELTA), deltaDiv, refDeltaDiv);
final double gammaDiv = gamma(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refGammaDiv = Math.max(Math.abs(gammaDiv), 1.) * 1.e-2;
assertEquals(resDiv.get(Greek.GAMMA), gammaDiv, refGammaDiv);
final double thetaDiv = theta(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double refThetaDiv = Math.max(Math.abs(thetaDiv), 1.) * 1.e-2;
assertEquals(resDiv.get(Greek.THETA), thetaDiv, refThetaDiv);
}
}
}
}
}
}
/**
* The dividend is cash or proportional to asset price
*/
@Test
public void greeksDiscreteDividendLatticeTest() {
final LatticeSpecification lattice = new TianLatticeSpecification();
final double[] propDividends = new double[] {0.01, 0.03, 0.02 };
final double[] cashDividends = new double[] {5., 10., 8. };
final double[] dividendTimes = new double[] {TIME / 601., TIME / 3., TIME / 2. };
final boolean[] tfSet = new boolean[] {true, false };
for (final boolean isCall : tfSet) {
for (final double strike : STRIKES) {
for (final double interest : INTERESTS) {
for (final double vol : VOLS) {
final int nSteps = 501;//1101 for all lattices
final int nStepsTri = 301;
final double resSpot = SPOT * (1. - propDividends[0]) * (1. - propDividends[1]) * (1. - propDividends[2]);
final double modSpot = SPOT - cashDividends[0] * Math.exp(-interest * dividendTimes[0]) - cashDividends[1] * Math.exp(-interest * dividendTimes[1]) - cashDividends[2] *
Math.exp(-interest * dividendTimes[2]);
final double exactPriceProp = price(resSpot, strike, TIME, vol, interest, interest, isCall);
final double exactDeltaProp = delta(resSpot, strike, TIME, vol, interest, interest, isCall);
final double exactGammaProp = gamma(resSpot, strike, TIME, vol, interest, interest, isCall);
final double exactThetaProp = theta(resSpot, strike, TIME, vol, interest, interest, isCall);
final double appPriceCash = price(modSpot, strike, TIME, vol, interest, interest, isCall);
final double appDeltaCash = delta(modSpot, strike, TIME, vol, interest, interest, isCall);
final double appGammaCash = gamma(modSpot, strike, TIME, vol, interest, interest, isCall);
final double appThetaCash = theta(modSpot, strike, TIME, vol, interest, interest, isCall);
final OptionFunctionProvider1D function = new AssetOrNothingOptionFunctionProvider(strike, TIME, nSteps, isCall);
final DividendFunctionProvider cashDividend = new CashDividendFunctionProvider(dividendTimes, cashDividends);
final DividendFunctionProvider propDividend = new ProportionalDividendFunctionProvider(dividendTimes, propDividends);
final GreekResultCollection resProp = _model.getGreeks(lattice, function, SPOT, vol, interest, propDividend);
final GreekResultCollection resCash = _model.getGreeks(lattice, function, SPOT, vol, interest, cashDividend);
assertEquals(resProp.get(Greek.FAIR_PRICE), exactPriceProp, Math.max(1., Math.abs(exactPriceProp)) * 1.e-1);
assertEquals(resProp.get(Greek.DELTA), exactDeltaProp, Math.max(1., Math.abs(exactDeltaProp)) * 1.e-1);
assertEquals(resProp.get(Greek.GAMMA), exactGammaProp, Math.max(1., Math.abs(exactGammaProp)) * 1.e-1);
assertEquals(resProp.get(Greek.THETA), exactThetaProp, Math.max(1., Math.abs(exactThetaProp)));//theta is poorly approximated
assertEquals(resCash.get(Greek.FAIR_PRICE), appPriceCash, Math.max(1., Math.abs(appPriceCash)) * 1.e-1);
assertEquals(resCash.get(Greek.DELTA), appDeltaCash, Math.max(1., Math.abs(appDeltaCash)) * 1.e-1);
assertEquals(resCash.get(Greek.GAMMA), appGammaCash, Math.max(1., Math.abs(appGammaCash)) * 1.e-1);
assertEquals(resCash.get(Greek.THETA), appThetaCash, Math.max(1., Math.abs(appThetaCash)));//theta is poorly approximated
final OptionFunctionProvider1D functionTri = new AssetOrNothingOptionFunctionProvider(strike, TIME, nStepsTri, isCall);
final GreekResultCollection greeksPropTrinomial = _modelTrinomial.getGreeks(lattice, functionTri, SPOT, vol, interest, propDividend);
final GreekResultCollection greeksCashTrinomial = _modelTrinomial.getGreeks(lattice, functionTri, SPOT, vol, interest, cashDividend);
assertEquals(greeksPropTrinomial.get(Greek.FAIR_PRICE), exactPriceProp, Math.max(1., Math.abs(exactPriceProp)) * 1.e-1);
assertEquals(greeksPropTrinomial.get(Greek.DELTA), exactDeltaProp, Math.max(1., Math.abs(exactDeltaProp)) * 1.e-1);
assertEquals(greeksPropTrinomial.get(Greek.GAMMA), exactGammaProp, Math.max(1., Math.abs(exactGammaProp)) * 1.e-1);
assertEquals(greeksPropTrinomial.get(Greek.THETA), exactThetaProp, Math.max(1., Math.abs(exactThetaProp)));//theta is poorly approximated
assertEquals(greeksCashTrinomial.get(Greek.FAIR_PRICE), appPriceCash, Math.max(1., Math.abs(appPriceCash)) * 1.e-1);
assertEquals(greeksCashTrinomial.get(Greek.DELTA), appDeltaCash, Math.max(1., Math.abs(appDeltaCash)) * 1.e-1);
assertEquals(greeksCashTrinomial.get(Greek.GAMMA), appGammaCash, Math.max(1., Math.abs(appGammaCash)) * 1.e-1);
assertEquals(greeksCashTrinomial.get(Greek.THETA), appThetaCash, Math.max(1., Math.abs(appThetaCash)));//theta is poorly approximated
}
}
}
}
}
/**
* non-constant volatility and interest rate
*/
@Test
public void timeVaryingVolTest() {
final LatticeSpecification lattice1 = new TimeVaryingLatticeSpecification();
final double[] time_set = new double[] {0.5, 1.2 };
final int steps = 801;
final double[] vol = new double[steps];
final double[] rate = new double[steps];
final double[] dividend = new double[steps];
final int stepsTri = 511;
final double[] volTri = new double[stepsTri];
final double[] rateTri = new double[stepsTri];
final double[] dividendTri = new double[stepsTri];
final double constA = 0.01;
final double constB = 0.001;
final double constC = 0.1;
final double constD = 0.05;
final boolean[] tfSet = new boolean[] {true, false };
for (final boolean isCall : tfSet) {
for (final double strike : STRIKES) {
for (final double time : time_set) {
for (int i = 0; i < steps; ++i) {
rate[i] = constA + constB * i * time / steps;
vol[i] = constC + constD * Math.sin(i * time / steps);
dividend[i] = 0.005;
}
for (int i = 0; i < stepsTri; ++i) {
rateTri[i] = constA + constB * i * time / steps;
volTri[i] = constC + constD * Math.sin(i * time / steps);
dividendTri[i] = 0.005;
}
final double rateRef = constA + 0.5 * constB * time;
final double volRef = Math.sqrt(constC * constC + 0.5 * constD * constD + 2. * constC * constD / time * (1. - Math.cos(time)) - constD * constD * 0.25 / time * Math.sin(2. * time));
final OptionFunctionProvider1D function = new AssetOrNothingOptionFunctionProvider(strike, time, steps, isCall);
final double resPrice = _model.getPrice(function, SPOT, vol, rate, dividend);
final GreekResultCollection resGreeks = _model.getGreeks(function, SPOT, vol, rate, dividend);
final double resPriceConst = _model.getPrice(lattice1, function, SPOT, volRef, rateRef, dividend[0]);
final GreekResultCollection resGreeksConst = _model.getGreeks(lattice1, function, SPOT, volRef, rateRef, dividend[0]);
assertEquals(resPrice, resPriceConst, Math.abs(resPriceConst) * 1.e-1);
assertEquals(resGreeks.get(Greek.FAIR_PRICE), resGreeksConst.get(Greek.FAIR_PRICE), Math.max(Math.abs(resGreeksConst.get(Greek.FAIR_PRICE)), 0.1) * 0.1);
assertEquals(resGreeks.get(Greek.DELTA), resGreeksConst.get(Greek.DELTA), Math.max(Math.abs(resGreeksConst.get(Greek.DELTA)), 0.1) * 0.1);
assertEquals(resGreeks.get(Greek.GAMMA), resGreeksConst.get(Greek.GAMMA), Math.max(Math.abs(resGreeksConst.get(Greek.GAMMA)), 0.1) * 0.1);
assertEquals(resGreeks.get(Greek.THETA), resGreeksConst.get(Greek.THETA), Math.max(Math.abs(resGreeksConst.get(Greek.THETA)), 0.1));
final OptionFunctionProvider1D functionTri = new AssetOrNothingOptionFunctionProvider(strike, time, stepsTri, isCall);
final double resPriceTrinomial = _modelTrinomial.getPrice(functionTri, SPOT, volTri, rateTri, dividendTri);
assertEquals(resPriceTrinomial, resPriceConst, Math.max(Math.abs(resPriceConst), .1) * 1.e-1);
final GreekResultCollection resGreeksTrinomial = _modelTrinomial.getGreeks(functionTri, SPOT, volTri, rateTri, dividendTri);
assertEquals(resGreeksTrinomial.get(Greek.FAIR_PRICE), resGreeksConst.get(Greek.FAIR_PRICE), Math.max(Math.abs(resGreeksConst.get(Greek.FAIR_PRICE)), 0.1) * 0.1);
assertEquals(resGreeksTrinomial.get(Greek.DELTA), resGreeksConst.get(Greek.DELTA), Math.max(Math.abs(resGreeksConst.get(Greek.DELTA)), 0.1) * 0.1);
assertEquals(resGreeksTrinomial.get(Greek.GAMMA), resGreeksConst.get(Greek.GAMMA), Math.max(Math.abs(resGreeksConst.get(Greek.GAMMA)), 0.1));
assertEquals(resGreeksTrinomial.get(Greek.THETA), resGreeksConst.get(Greek.THETA), Math.max(Math.abs(resGreeksConst.get(Greek.THETA)), 0.1));
}
}
}
}
/**
*
*/
@Test
public void hashCodeEqualsTest() {
final OptionFunctionProvider1D ref = new AssetOrNothingOptionFunctionProvider(100., 1., 53, true);
final OptionFunctionProvider1D[] function = new OptionFunctionProvider1D[] {ref, new AssetOrNothingOptionFunctionProvider(100., 1., 53, true),
new AmericanVanillaOptionFunctionProvider(100., 1., 53, true), null };
final int len = function.length;
for (int i = 0; i < len; ++i) {
if (ref.equals(function[i])) {
assertTrue(ref.hashCode() == function[i].hashCode());
}
}
for (int i = 0; i < len - 1; ++i) {
assertTrue(function[i].equals(ref) == ref.equals(function[i]));
}
assertFalse(ref.equals(new EuropeanSpreadOptionFunctionProvider(110., 1., 53, true)));
}
private double price(final double spot, final double strike, final double time, final double vol, final double interest, final double cost, final boolean isCall) {
final double d = (Math.log(spot / strike) + (cost + 0.5 * vol * vol) * time) / vol / Math.sqrt(time);
final double sign = isCall ? 1. : -1.;
return spot * Math.exp((cost - interest) * time) * NORMAL.getCDF(sign * d);
}
private double delta(final double spot, final double strike, final double time, final double vol, final double interest, final double cost, final boolean isCall) {
final double d = (Math.log(spot / strike) + (cost + 0.5 * vol * vol) * time) / vol / Math.sqrt(time);
final double sign = isCall ? 1. : -1.;
return Math.exp((cost - interest) * time) * (NORMAL.getCDF(sign * d) + sign * NORMAL.getPDF(d) / vol / Math.sqrt(time));
}
private double gamma(final double spot, final double strike, final double time, final double vol, final double interest, final double cost, final boolean isCall) {
final double d = (Math.log(spot / strike) + (cost + 0.5 * vol * vol) * time) / vol / Math.sqrt(time);
final double sign = isCall ? 1. : -1.;
return sign * (Math.exp((cost - interest) * time) * NORMAL.getPDF(d) * (1. - d / vol / Math.sqrt(time)) / spot / vol / Math.sqrt(time));
}
private double theta(final double spot, final double strike, final double time, final double vol, final double interest, final double cost, final boolean isCall) {
final double d = (Math.log(spot / strike) + (cost + 0.5 * vol * vol) * time) / vol / Math.sqrt(time);
final double sign = isCall ? 1. : -1.;
final double div = 0.5 * (-Math.log(spot / strike) / Math.pow(time, 1.5) + (cost + 0.5 * vol * vol) / Math.pow(time, 0.5)) / vol;
return -spot * (cost - interest) * Math.exp((cost - interest) * time) * NORMAL.getCDF(sign * d) - sign * spot * Math.exp((cost - interest) * time) * NORMAL.getPDF(d) * div;
}
/**
* test for analytic formula
*/
@Test(enabled = false)
public void functionTest() {
final boolean[] tfSet = new boolean[] {true, false };
final double eps = 1.e-6;
for (final boolean isCall : tfSet) {
for (final double strike : STRIKES) {
for (final double interest : INTERESTS) {
for (final double vol : VOLS) {
for (final double dividend : DIVIDENDS) {
final double delta = delta(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double gamma = gamma(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double theta = theta(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
final double upSpot = price(SPOT + eps, strike, TIME, vol, interest, interest - dividend, isCall);
final double downSpot = price(SPOT - eps, strike, TIME, vol, interest, interest - dividend, isCall);
final double upSpotDelta = delta(SPOT + eps, strike, TIME, vol, interest, interest - dividend, isCall);
final double downSpotDelta = delta(SPOT - eps, strike, TIME, vol, interest, interest - dividend, isCall);
final double upTime = price(SPOT, strike, TIME + eps, vol, interest, interest - dividend, isCall);
final double downTime = price(SPOT, strike, TIME - eps, vol, interest, interest - dividend, isCall);
assertEquals(delta, 0.5 * (upSpot - downSpot) / eps, eps);
assertEquals(gamma, 0.5 * (upSpotDelta - downSpotDelta) / eps, eps);
assertEquals(theta, -0.5 * (upTime - downTime) / eps, eps);
}
}
}
}
}
}
}