public void testFdEuropeanValues() { // Testing finite-difference dividend European option values... using (SavedSettings backup = new SavedSettings()) { double tolerance = 1.0e-2; int gridPoints = 300; int timeSteps = 40; Option.Type[] types = { Option.Type.Call, Option.Type.Put }; double[] strikes = { 50.0, 99.5, 100.0, 100.5, 150.0 }; double[] underlyings = { 100.0 }; // Rate qRates[] = { 0.00, 0.10, 0.30 }; // Analytic dividend may not be handling q correctly double[] qRates = { 0.00 }; double[] rRates = { 0.01, 0.05, 0.15 }; int[] lengths = { 1, 2 }; double[] vols = { 0.05, 0.20, 0.40 }; DayCounter dc = new Actual360(); Date today = Date.Today; Settings.setEvaluationDate(today); SimpleQuote spot = new SimpleQuote(0.0); SimpleQuote qRate = new SimpleQuote(0.0); Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(qRate, dc)); SimpleQuote rRate = new SimpleQuote(0.0); Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(rRate, dc)); SimpleQuote vol = new SimpleQuote(0.0); Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(vol, dc)); for (int i = 0; i < types.Length; i++) { for (int j = 0; j < strikes.Length; j++) { for (int k = 0; k < lengths.Length; k++) { Date exDate = today + new Period(lengths[k], TimeUnit.Years); Exercise exercise = new EuropeanExercise(exDate); List <Date> dividendDates = new List <Date>(); List <double> dividends = new List <double>(); for (Date d = today + new Period(3, TimeUnit.Months); d < exercise.lastDate(); d += new Period(6, TimeUnit.Months)) { dividendDates.Add(d); dividends.Add(5.0); } StrikedTypePayoff payoff = new PlainVanillaPayoff(types[i], strikes[j]); BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot), qTS, rTS, volTS); IPricingEngine engine = new FDDividendEuropeanEngine(stochProcess, timeSteps, gridPoints); IPricingEngine ref_engine = new AnalyticDividendEuropeanEngine(stochProcess); DividendVanillaOption option = new DividendVanillaOption(payoff, exercise, dividendDates, dividends); option.setPricingEngine(engine); DividendVanillaOption ref_option = new DividendVanillaOption(payoff, exercise, dividendDates, dividends); ref_option.setPricingEngine(ref_engine); for (int l = 0; l < underlyings.Length; l++) { for (int m = 0; m < qRates.Length; m++) { for (int n = 0; n < rRates.Length; n++) { for (int p = 0; p < vols.Length; p++) { double u = underlyings[l]; double q = qRates[m], r = rRates[n]; double v = vols[p]; spot.setValue(u); qRate.setValue(q); rRate.setValue(r); vol.setValue(v); // FLOATING_POINT_EXCEPTION double calculated = option.NPV(); if (calculated > spot.value() * 1.0e-5) { double expected = ref_option.NPV(); double error = Math.Abs(calculated - expected); if (error > tolerance) { REPORT_FAILURE("value", payoff, exercise, u, q, r, today, v, expected, calculated, error, tolerance); } } } } } } } } } } }
private void testFdGreeks <Engine>(Date today, Exercise exercise) where Engine : IFDEngine, new () { Dictionary <string, double> calculated = new Dictionary <string, double>(), expected = new Dictionary <string, double>(), tolerance = new Dictionary <string, double>(); tolerance.Add("delta", 5.0e-3); tolerance.Add("gamma", 7.0e-3); // tolerance["theta"] = 1.0e-2; Option.Type[] types = { Option.Type.Call, Option.Type.Put }; double[] strikes = { 50.0, 99.5, 100.0, 100.5, 150.0 }; double[] underlyings = { 100.0 }; double[] qRates = { 0.00, 0.10, 0.20 }; double[] rRates = { 0.01, 0.05, 0.15 }; double[] vols = { 0.05, 0.20, 0.50 }; DayCounter dc = new Actual360(); SimpleQuote spot = new SimpleQuote(0.0); SimpleQuote qRate = new SimpleQuote(0.0); Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(qRate, dc)); SimpleQuote rRate = new SimpleQuote(0.0); Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(rRate, dc)); SimpleQuote vol = new SimpleQuote(0.0); Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(vol, dc)); for (int i = 0; i < types.Length; i++) { for (int j = 0; j < strikes.Length; j++) { List <Date> dividendDates = new List <Date>(); List <double> dividends = new List <double>(); for (Date d = today + new Period(3, TimeUnit.Months); d < exercise.lastDate(); d += new Period(6, TimeUnit.Months)) { dividendDates.Add(d); dividends.Add(5.0); } StrikedTypePayoff payoff = new PlainVanillaPayoff(types[i], strikes[j]); BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot), qTS, rTS, volTS); IPricingEngine engine = FastActivator <Engine> .Create().factory(stochProcess); DividendVanillaOption option = new DividendVanillaOption(payoff, exercise, dividendDates, dividends); option.setPricingEngine(engine); for (int l = 0; l < underlyings.Length; l++) { for (int m = 0; m < qRates.Length; m++) { for (int n = 0; n < rRates.Length; n++) { for (int p = 0; p < vols.Length; p++) { double u = underlyings[l]; double q = qRates[m], r = rRates[n]; double v = vols[p]; spot.setValue(u); qRate.setValue(q); rRate.setValue(r); vol.setValue(v); // FLOATING_POINT_EXCEPTION double value = option.NPV(); calculated["delta"] = option.delta(); calculated["gamma"] = option.gamma(); // calculated["theta"] = option.theta(); if (value > spot.value() * 1.0e-5) { // perturb spot and get delta and gamma double du = u * 1.0e-4; spot.setValue(u + du); double value_p = option.NPV(), delta_p = option.delta(); spot.setValue(u - du); double value_m = option.NPV(), delta_m = option.delta(); spot.setValue(u); expected["delta"] = (value_p - value_m) / (2 * du); expected["gamma"] = (delta_p - delta_m) / (2 * du); // perturb date and get theta /* * Time dT = dc.yearFraction(today-1, today+1); * Settings::instance().evaluationDate() = today-1; * value_m = option.NPV(); * Settings::instance().evaluationDate() = today+1; * value_p = option.NPV(); * Settings::instance().evaluationDate() = today; * expected["theta"] = (value_p - value_m)/dT; */ // compare foreach (string greek in calculated.Keys) { double expct = expected[greek], calcl = calculated[greek], tol = tolerance[greek]; double error = Utilities.relativeError(expct, calcl, u); if (error > tol) { REPORT_FAILURE(greek, payoff, exercise, u, q, r, today, v, expct, calcl, error, tol); } } } } } } } } } }
public void testEuropeanGreeks() { // Testing dividend European option greeks... using (SavedSettings backup = new SavedSettings()) { Dictionary <string, double> calculated = new Dictionary <string, double>(), expected = new Dictionary <string, double>(), tolerance = new Dictionary <string, double>(); tolerance["delta"] = 1.0e-5; tolerance["gamma"] = 1.0e-5; tolerance["theta"] = 1.0e-5; tolerance["rho"] = 1.0e-5; tolerance["vega"] = 1.0e-5; Option.Type[] types = { Option.Type.Call, Option.Type.Put }; double[] strikes = { 50.0, 99.5, 100.0, 100.5, 150.0 }; double[] underlyings = { 100.0 }; double[] qRates = { 0.00, 0.10, 0.30 }; double[] rRates = { 0.01, 0.05, 0.15 }; int[] lengths = { 1, 2 }; double[] vols = { 0.05, 0.20, 0.40 }; DayCounter dc = new Actual360(); Date today = Date.Today; Settings.setEvaluationDate(today); SimpleQuote spot = new SimpleQuote(0.0); SimpleQuote qRate = new SimpleQuote(0.0); Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(qRate, dc)); SimpleQuote rRate = new SimpleQuote(0.0); Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(rRate, dc)); SimpleQuote vol = new SimpleQuote(0.0); Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(vol, dc)); for (int i = 0; i < types.Length; i++) { for (int j = 0; j < strikes.Length; j++) { for (int k = 0; k < lengths.Length; k++) { Date exDate = today + new Period(lengths[k], TimeUnit.Years); Exercise exercise = new EuropeanExercise(exDate); List <Date> dividendDates = new List <Date>(); List <double> dividends = new List <double>(); for (Date d = today + new Period(3, TimeUnit.Months); d < exercise.lastDate(); d += new Period(6, TimeUnit.Months)) { dividendDates.Add(d); dividends.Add(5.0); } StrikedTypePayoff payoff = new PlainVanillaPayoff(types[i], strikes[j]); BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot), qTS, rTS, volTS); IPricingEngine engine = new AnalyticDividendEuropeanEngine(stochProcess); DividendVanillaOption option = new DividendVanillaOption(payoff, exercise, dividendDates, dividends); option.setPricingEngine(engine); for (int l = 0; l < underlyings.Length; l++) { for (int m = 0; m < qRates.Length; m++) { for (int n = 0; n < rRates.Length; n++) { for (int p = 0; p < vols.Length; p++) { double u = underlyings[l]; double q = qRates[m], r = rRates[n]; double v = vols[p]; spot.setValue(u); qRate.setValue(q); rRate.setValue(r); vol.setValue(v); double value = option.NPV(); calculated["delta"] = option.delta(); calculated["gamma"] = option.gamma(); calculated["theta"] = option.theta(); calculated["rho"] = option.rho(); calculated["vega"] = option.vega(); if (value > spot.value() * 1.0e-5) { // perturb spot and get delta and gamma double du = u * 1.0e-4; spot.setValue(u + du); double value_p = option.NPV(), delta_p = option.delta(); spot.setValue(u - du); double value_m = option.NPV(), delta_m = option.delta(); spot.setValue(u); expected["delta"] = (value_p - value_m) / (2 * du); expected["gamma"] = (delta_p - delta_m) / (2 * du); // perturb risk-free rate and get rho double dr = r * 1.0e-4; rRate.setValue(r + dr); value_p = option.NPV(); rRate.setValue(r - dr); value_m = option.NPV(); rRate.setValue(r); expected["rho"] = (value_p - value_m) / (2 * dr); // perturb volatility and get vega double dv = v * 1.0e-4; vol.setValue(v + dv); value_p = option.NPV(); vol.setValue(v - dv); value_m = option.NPV(); vol.setValue(v); expected["vega"] = (value_p - value_m) / (2 * dv); // perturb date and get theta double dT = dc.yearFraction(today - 1, today + 1); Settings.setEvaluationDate(today - 1); value_m = option.NPV(); Settings.setEvaluationDate(today + 1); value_p = option.NPV(); Settings.setEvaluationDate(today); expected["theta"] = (value_p - value_m) / dT; // compare foreach (KeyValuePair <string, double> it in calculated) { string greek = it.Key; double expct = expected[greek], calcl = calculated[greek], tol = tolerance[greek]; double error = Utilities.relativeError(expct, calcl, u); if (error > tol) { REPORT_FAILURE(greek, payoff, exercise, u, q, r, today, v, expct, calcl, error, tol); } } } } } } } } } } } }
public void testEuropeanStartLimit() { // Testing dividend European option with a dividend on today's date... using (SavedSettings backup = new SavedSettings()) { double tolerance = 1.0e-5; double dividendValue = 10.0; Option.Type[] types = { Option.Type.Call, Option.Type.Put }; double[] strikes = { 50.0, 99.5, 100.0, 100.5, 150.0 }; double[] underlyings = { 100.0 }; double[] qRates = { 0.00, 0.10, 0.30 }; double[] rRates = { 0.01, 0.05, 0.15 }; int[] lengths = { 1, 2 }; double[] vols = { 0.05, 0.20, 0.70 }; DayCounter dc = new Actual360(); Date today = Date.Today; Settings.setEvaluationDate(today); SimpleQuote spot = new SimpleQuote(0.0); SimpleQuote qRate = new SimpleQuote(0.0); Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(qRate, dc)); SimpleQuote rRate = new SimpleQuote(0.0); Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(rRate, dc)); SimpleQuote vol = new SimpleQuote(0.0); Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(vol, dc)); for (int i = 0; i < types.Length; i++) { for (int j = 0; j < strikes.Length; j++) { for (int k = 0; k < lengths.Length; k++) { Date exDate = today + new Period(lengths[k], TimeUnit.Years); Exercise exercise = new EuropeanExercise(exDate); List <Date> dividendDates = new List <Date>(); List <double> dividends = new List <double>(); dividendDates.Add(today); dividends.Add(dividendValue); StrikedTypePayoff payoff = new PlainVanillaPayoff(types[i], strikes[j]); BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot), qTS, rTS, volTS); IPricingEngine engine = new AnalyticDividendEuropeanEngine(stochProcess); IPricingEngine ref_engine = new AnalyticEuropeanEngine(stochProcess); DividendVanillaOption option = new DividendVanillaOption(payoff, exercise, dividendDates, dividends); option.setPricingEngine(engine); VanillaOption ref_option = new VanillaOption(payoff, exercise); ref_option.setPricingEngine(ref_engine); for (int l = 0; l < underlyings.Length; l++) { for (int m = 0; m < qRates.Length; m++) { for (int n = 0; n < rRates.Length; n++) { for (int p = 0; p < vols.Length; p++) { double u = underlyings[l]; double q = qRates[m], r = rRates[n]; double v = vols[p]; spot.setValue(u); qRate.setValue(q); rRate.setValue(r); vol.setValue(v); double calculated = option.NPV(); spot.setValue(u - dividendValue); double expected = ref_option.NPV(); double error = Math.Abs(calculated - expected); if (error > tolerance) { REPORT_FAILURE("value", payoff, exercise, u, q, r, today, v, expected, calculated, error, tolerance); } } } } } } } } } }
// Reference pg. 253 - Hull - Options, Futures, and Other Derivatives 5th ed // Exercise 12.8 // Doesn't quite work. Need to deal with date conventions private void testEuropeanKnownValue() { // Testing dividend European option values with known value... using (SavedSettings backup = new SavedSettings()) { double tolerance = 1.0e-2; double expected = 3.67; DayCounter dc = new Actual360(); Date today = Date.Today; Settings.setEvaluationDate(today); SimpleQuote spot = new SimpleQuote(0.0); SimpleQuote qRate = new SimpleQuote(0.0); Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(qRate, dc)); SimpleQuote rRate = new SimpleQuote(0.0); Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(rRate, dc)); SimpleQuote vol = new SimpleQuote(0.0); Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(vol, dc)); Date exDate = today + new Period(6, TimeUnit.Months); Exercise exercise = new EuropeanExercise(exDate); List <Date> dividendDates = new List <Date>(); List <double> dividends = new List <double>(); dividendDates.Add(today + new Period(2, TimeUnit.Months)); dividends.Add(0.50); dividendDates.Add(today + new Period(5, TimeUnit.Months)); dividends.Add(0.50); StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Call, 40.0); BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot), qTS, rTS, volTS); IPricingEngine engine = new AnalyticDividendEuropeanEngine(stochProcess); DividendVanillaOption option = new DividendVanillaOption(payoff, exercise, dividendDates, dividends); option.setPricingEngine(engine); double u = 40.0; double q = 0.0, r = 0.09; double v = 0.30; spot.setValue(u); qRate.setValue(q); rRate.setValue(r); vol.setValue(v); double calculated = option.NPV(); double error = Math.Abs(calculated - expected); if (error > tolerance) { REPORT_FAILURE("value start limit", payoff, exercise, u, q, r, today, v, expected, calculated, error, tolerance); } } }
private void testFdDegenerate <Engine>(Date today, Exercise exercise) where Engine : IFDEngine, new () { DayCounter dc = new Actual360(); SimpleQuote spot = new SimpleQuote(54.625); Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.052706, dc)); Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.0, dc)); Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(0.282922, dc)); BlackScholesMertonProcess process = new BlackScholesMertonProcess(new Handle <Quote>(spot), qTS, rTS, volTS); int timeSteps = 300; int gridPoints = 300; IPricingEngine engine = FastActivator <Engine> .Create().factory(process, timeSteps, gridPoints); StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Call, 55.0); double tolerance = 3.0e-3; List <double> dividends = new List <double>(); List <Date> dividendDates = new List <Date>(); DividendVanillaOption option1 = new DividendVanillaOption(payoff, exercise, dividendDates, dividends); option1.setPricingEngine(engine); // FLOATING_POINT_EXCEPTION double refValue = option1.NPV(); for (int i = 0; i <= 6; i++) { dividends.Add(0.0); dividendDates.Add(today + i); DividendVanillaOption option = new DividendVanillaOption(payoff, exercise, dividendDates, dividends); option.setPricingEngine(engine); double value = option.NPV(); if (Math.Abs(refValue - value) > tolerance) { QAssert.Fail("NPV changed by null dividend :\n" + " previous value: " + value + "\n" + " current value: " + refValue + "\n" + " change: " + (value - refValue)); } } }