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));
}
}
}
