Java tutorial
/** * Copyright (C) 2009 - 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.AssertJUnit.assertEquals; import org.apache.commons.lang.Validate; import org.testng.annotations.Test; import org.threeten.bp.ZonedDateTime; import com.opengamma.analytics.financial.model.interestrate.curve.YieldAndDiscountCurve; import com.opengamma.analytics.financial.model.interestrate.curve.YieldCurve; import com.opengamma.analytics.financial.model.option.definition.EuropeanVanillaOptionDefinition; import com.opengamma.analytics.financial.model.option.definition.GeneralLogNormalOptionDataBundle; import com.opengamma.analytics.financial.model.option.definition.OptionDefinition; import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.BlackFunctionData; import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.CEVFunctionData; import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.CEVPriceFunction; import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.EuropeanVanillaOption; import com.opengamma.analytics.financial.model.tree.RecombiningBinomialTree; import com.opengamma.analytics.financial.model.volatility.BlackImpliedVolatilityFormula; import com.opengamma.analytics.financial.model.volatility.surface.DriftSurface; import com.opengamma.analytics.financial.model.volatility.surface.VolatilitySurface; import com.opengamma.analytics.math.curve.ConstantDoublesCurve; import com.opengamma.analytics.math.function.Function; import com.opengamma.analytics.math.surface.FunctionalDoublesSurface; import com.opengamma.util.time.DateUtils; import com.opengamma.util.time.Expiry; /** * */ public class LogNormalBinomialTreeBuilderTest { private static final double SPOT = 100; private static final double FORWARD; private static final double T = 5.0; private static final double BETA = 0.4; private static final YieldAndDiscountCurve YIELD_CURVE = YieldCurve.from(ConstantDoublesCurve.from(0.05)); private static final double ATM_VOL = 0.20; private static final double SIGMA_BETA; private static final ZonedDateTime DATE = DateUtils.getUTCDate(2010, 7, 1); private static final OptionDefinition OPTION; private static final BinomialTreeBuilder<GeneralLogNormalOptionDataBundle> BUILDER = new LogNormalBinomialTreeBuilder<>(); private static final DriftSurface DRIFTLESS; private static final BlackImpliedVolatilityFormula BLACK_IMPLIED_VOL = new BlackImpliedVolatilityFormula(); private static final CEVPriceFunction CEV_PRICE = new CEVPriceFunction(); static { SIGMA_BETA = ATM_VOL * Math.pow(SPOT, 1 - BETA); FORWARD = SPOT / YIELD_CURVE.getDiscountFactor(T); OPTION = new EuropeanVanillaOptionDefinition(FORWARD, new Expiry(DateUtils.getDateOffsetWithYearFraction(DATE, T)), true); final Function<Double, Double> driftless = new Function<Double, Double>() { @Override public Double evaluate(final Double... tk) { Validate.isTrue(tk.length == 2); return 0.0; } }; DRIFTLESS = new DriftSurface(FunctionalDoublesSurface.from(driftless)); } private static final Function<Double, Double> FLAT_LOCAL_VOL = new Function<Double, Double>() { @Override public Double evaluate(final Double... tk) { Validate.isTrue(tk.length == 2); return ATM_VOL; } }; private static final Function<Double, Double> TIME_DEPENDENT_LOCAL_VOL = new Function<Double, Double>() { @Override public Double evaluate(final Double... tk) { Validate.isTrue(tk.length == 2); final double t = tk[0]; return (2 * ATM_VOL - t * ATM_VOL / T); } }; private static final Function<Double, Double> CEV_LOCAL_VOL = new Function<Double, Double>() { @SuppressWarnings("synthetic-access") @Override public Double evaluate(final Double... tk) { Validate.isTrue(tk.length == 2); final double f = tk[1]; final double sigma = SIGMA_BETA * Math.pow(f, BETA - 1); // return Math.min(sigma,100*ATM_VOL); return sigma; } }; private static final GeneralLogNormalOptionDataBundle DATA = new GeneralLogNormalOptionDataBundle(YIELD_CURVE, DRIFTLESS, new VolatilitySurface(FunctionalDoublesSurface.from(FLAT_LOCAL_VOL)), FORWARD, DATE); @Test public void testPriceFlat() { final RecombiningBinomialTree<BinomialTreeNode<Double>> assetPriceTree = BUILDER.buildAssetTree(T, DATA, 200); RecombiningBinomialTree<BinomialTreeNode<Double>> optionPriceTree = BUILDER.buildOptionPriceTree(OPTION, DATA, assetPriceTree); EuropeanVanillaOption o = new EuropeanVanillaOption(FORWARD, T, true); final BlackFunctionData data = new BlackFunctionData(FORWARD, YIELD_CURVE.getDiscountFactor(T), 0); double impVol = BLACK_IMPLIED_VOL.getImpliedVolatility(data, o, optionPriceTree.getNode(0, 0).getValue()); //double impVol = BlackImpliedVolFormula.impliedVol(optionPriceTree.getNode(0, 0).getValue(), FORWARD, FORWARD, YIELD_CURVE.getDiscountFactor(T), T, true); assertEquals(ATM_VOL, impVol, 1e-3); for (int i = 0; i < 10; i++) { final double m = -1.5 + 3.0 * i / 10.0; final double strike = FORWARD * Math.exp(ATM_VOL * Math.sqrt(T) * m); final OptionDefinition option = new EuropeanVanillaOptionDefinition(strike, OPTION.getExpiry(), OPTION.isCall()); optionPriceTree = BUILDER.buildOptionPriceTree(option, DATA, assetPriceTree); o = new EuropeanVanillaOption(strike, T, OPTION.isCall()); optionPriceTree = BUILDER.buildOptionPriceTree(option, DATA, assetPriceTree); impVol = BLACK_IMPLIED_VOL.getImpliedVolatility(data, o, optionPriceTree.getNode(0, 0).getValue()); // impVol = BlackImpliedVolFormula.impliedVol(optionPriceTree.getNode(0, 0).getValue(), FORWARD, strike, YIELD_CURVE.getDiscountFactor(T), T, true); // System.out.println(strike+"\t"+impVol); assertEquals(ATM_VOL, impVol, 1e-3); } } @Test public void testPriceTimeDependent() { final GeneralLogNormalOptionDataBundle data = new GeneralLogNormalOptionDataBundle(YIELD_CURVE, DRIFTLESS, new VolatilitySurface(FunctionalDoublesSurface.from(TIME_DEPENDENT_LOCAL_VOL)), FORWARD, DATE); final RecombiningBinomialTree<BinomialTreeNode<Double>> assetPriceTree = BUILDER.buildAssetTree(T, data, 200); RecombiningBinomialTree<BinomialTreeNode<Double>> optionPriceTree = BUILDER.buildOptionPriceTree(OPTION, data, assetPriceTree); final double vol = Math.sqrt(7.0 / 3.0) * ATM_VOL; EuropeanVanillaOption o = new EuropeanVanillaOption(FORWARD, T, true); final BlackFunctionData bfd = new BlackFunctionData(FORWARD, YIELD_CURVE.getDiscountFactor(T), 0); double impVol = BLACK_IMPLIED_VOL.getImpliedVolatility(bfd, o, optionPriceTree.getNode(0, 0).getValue()); // double impVol = BlackImpliedVolFormula.impliedVol(optionPriceTree.getNode(0, 0).getValue(), FORWARD, FORWARD, df, T, true); assertEquals(vol, impVol, 1e-3); for (int i = 0; i < 10; i++) { final double m = -1.5 + 3.0 * i / 10.0; final double strike = FORWARD * Math.exp(ATM_VOL * Math.sqrt(T) * m); final OptionDefinition option = new EuropeanVanillaOptionDefinition(strike, OPTION.getExpiry(), OPTION.isCall()); optionPriceTree = BUILDER.buildOptionPriceTree(option, data, assetPriceTree); o = new EuropeanVanillaOption(strike, T, OPTION.isCall()); optionPriceTree = BUILDER.buildOptionPriceTree(option, DATA, assetPriceTree); impVol = BLACK_IMPLIED_VOL.getImpliedVolatility(bfd, o, optionPriceTree.getNode(0, 0).getValue()); // impVol = BlackImpliedVolFormula.impliedVol(optionPriceTree.getNode(0, 0).getValue(), FORWARD, strike, df, T, true); // System.out.println(strike+"\t"+impVol); assertEquals(vol, impVol, 1e-3); } } @Test public void testCEV() { final GeneralLogNormalOptionDataBundle data = new GeneralLogNormalOptionDataBundle(YIELD_CURVE, DRIFTLESS, new VolatilitySurface(FunctionalDoublesSurface.from(CEV_LOCAL_VOL)), FORWARD, DATE); final RecombiningBinomialTree<BinomialTreeNode<Double>> assetPriceTree = BUILDER.buildAssetTree(T, data, 200); RecombiningBinomialTree<BinomialTreeNode<Double>> optionPriceTree = BUILDER.buildOptionPriceTree(OPTION, data, assetPriceTree); EuropeanVanillaOption o = new EuropeanVanillaOption(FORWARD, T, true); final CEVFunctionData cfd = new CEVFunctionData(FORWARD, YIELD_CURVE.getDiscountFactor(T), SIGMA_BETA, BETA); for (int i = 0; i < 10; i++) { final double m = -1.5 + 3.0 * i / 10.0; final double strike = FORWARD * Math.exp(ATM_VOL * Math.sqrt(T) * m); final OptionDefinition option = new EuropeanVanillaOptionDefinition(strike, OPTION.getExpiry(), OPTION.isCall()); optionPriceTree = BUILDER.buildOptionPriceTree(option, data, assetPriceTree); o = new EuropeanVanillaOption(strike, T, true); final double cevPrice = CEV_PRICE.getPriceFunction(o).evaluate(cfd); final double cevVol = BLACK_IMPLIED_VOL.getImpliedVolatility( new BlackFunctionData(FORWARD, YIELD_CURVE.getDiscountFactor(T), SIGMA_BETA), o, cevPrice); final double impVol = BLACK_IMPLIED_VOL.getImpliedVolatility( new BlackFunctionData(FORWARD, YIELD_CURVE.getDiscountFactor(T), SIGMA_BETA), o, optionPriceTree.getNode(0, 0).getValue()); // final double cevPrice = CEVFormula.optionPrice(FORWARD, strike, BETA, df, SIGMA_BETA, T, true); // final double cevVol = BlackImpliedVolFormula.impliedVol(cevPrice, FORWARD, strike, df, T, true); // final double impVol = BlackImpliedVolFormula.impliedVol(optionPriceTree.getNode(0, 0).getValue(), FORWARD, strike, df, T, true); // System.out.println(strike + "\t" + cevVol + "\t" + impVol); assertEquals(cevVol, impVol, 1e-3); } } }