public void testAnalyticContinuousGeometricAveragePrice()
{
//("Testing analytic continuous geometric average-price Asians...");
// data from "Option Pricing Formulas", Haug, pag.96-97
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(80.0);
SimpleQuote qRate = new SimpleQuote(-0.03);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.05);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.20);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
BlackScholesMertonProcess stochProcess = new
BlackScholesMertonProcess(new Handle<Quote>(spot),
new Handle<YieldTermStructure>(qTS),
new Handle<YieldTermStructure>(rTS),
new Handle<BlackVolTermStructure>(volTS));
IPricingEngine engine = new
AnalyticContinuousGeometricAveragePriceAsianEngine(stochProcess);
Average.Type averageType = Average.Type.Geometric;
Option.Type type = Option.Type.Put;
double strike = 85.0;
Date exerciseDate = today + 90;
int pastFixings = 0; //Null<int>();
double runningAccumulator = 0.0; //Null<Real>();
StrikedTypePayoff payoff = new PlainVanillaPayoff(type, strike);
Exercise exercise = new EuropeanExercise(exerciseDate);
ContinuousAveragingAsianOption option =
new ContinuousAveragingAsianOption(averageType, payoff, exercise);
option.setPricingEngine(engine);
double calculated = option.NPV();
double expected = 4.6922;
double tolerance = 1.0e-4;
if (Math.Abs(calculated - expected) > tolerance)
{
REPORT_FAILURE("value", averageType, runningAccumulator, pastFixings,
new List<Date>(), payoff, exercise, spot.value(),
qRate.value(), rRate.value(), today,
vol.value(), expected, calculated, tolerance);
}
// trying to approximate the continuous version with the discrete version
runningAccumulator = 1.0;
pastFixings = 0;
List<Date> fixingDates = new InitializedList<Date>(exerciseDate - today + 1);
for (int i = 0; i < fixingDates.Count; i++)
{
fixingDates[i] = today + i;
}
IPricingEngine engine2 = new
AnalyticDiscreteGeometricAveragePriceAsianEngine(stochProcess);
DiscreteAveragingAsianOption option2 =
new DiscreteAveragingAsianOption(averageType,
runningAccumulator, pastFixings,
fixingDates,
payoff,
exercise);
option2.setPricingEngine(engine2);
calculated = option2.NPV();
tolerance = 3.0e-3;
/*if (Math.Abs(calculated - expected) > tolerance)
{
REPORT_FAILURE("value", averageType, runningAccumulator, pastFixings,
fixingDates, payoff, exercise, spot.value(),
qRate.value(), rRate.value(), today,
vol.value(), expected, calculated, tolerance);
}*/
}
public void testPastFixings()
{
//BOOST_MESSAGE("Testing use of past fixings in Asian options...");
DayCounter dc = new Actual360();
Date today = Date.Today ;
SimpleQuote spot = new SimpleQuote(100.0);
SimpleQuote qRate = new SimpleQuote(0.03);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.06);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.20);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Put, 100.0);
Exercise exercise = new EuropeanExercise(today + new Period(1,TimeUnit.Years));
BlackScholesMertonProcess stochProcess =
new BlackScholesMertonProcess(new Handle<Quote>(spot),
new Handle<YieldTermStructure>(qTS),
new Handle<YieldTermStructure>(rTS),
new Handle<BlackVolTermStructure>(volTS));
// MC arithmetic average-price
double runningSum = 0.0;
int pastFixings = 0;
List<Date> fixingDates1 = new InitializedList<Date>();
for (int i=0; i<=12; ++i)
fixingDates1.Add(today + new Period(i,TimeUnit.Months));
DiscreteAveragingAsianOption option1 =
new DiscreteAveragingAsianOption(Average.Type.Arithmetic, runningSum,
pastFixings, fixingDates1,
payoff, exercise);
pastFixings = 2;
runningSum = pastFixings * spot.value() * 0.8;
List<Date> fixingDates2 = new InitializedList<Date>();
for (int i=-2; i<=12; ++i)
fixingDates2.Add(today + new Period(i,TimeUnit.Months));
DiscreteAveragingAsianOption option2 =
new DiscreteAveragingAsianOption(Average.Type.Arithmetic, runningSum,
pastFixings, fixingDates2,
payoff, exercise);
IPricingEngine engine =
new MakeMCDiscreteArithmeticAPEngine<LowDiscrepancy,Statistics>(stochProcess)
.withStepsPerYear(1)
.withSamples(2047)
.value() ;
option1.setPricingEngine(engine);
option2.setPricingEngine(engine);
double price1 = option1.NPV();
double price2 = option2.NPV();
if (Utils.close(price1, price2)) {
Assert.Fail(
"past fixings had no effect on arithmetic average-price option"
+ "\n without fixings: " + price1
+ "\n with fixings: " + price2);
}
// MC arithmetic average-strike
engine = new MakeMCDiscreteArithmeticASEngine<LowDiscrepancy,Statistics>(stochProcess)
.withSamples(2047)
.value();
option1.setPricingEngine(engine);
option2.setPricingEngine(engine);
price1 = option1.NPV();
price2 = option2.NPV();
if (Utils.close(price1, price2)) {
Assert.Fail(
"past fixings had no effect on arithmetic average-strike option"
+ "\n without fixings: " + price1
+ "\n with fixings: " + price2);
}
// analytic geometric average-price
double runningProduct = 1.0;
pastFixings = 0;
DiscreteAveragingAsianOption option3 =
new DiscreteAveragingAsianOption(Average.Type.Geometric, runningProduct,
pastFixings, fixingDates1,
payoff, exercise);
pastFixings = 2;
runningProduct = spot.value() * spot.value();
DiscreteAveragingAsianOption option4 =
new DiscreteAveragingAsianOption(Average.Type.Geometric, runningProduct,
pastFixings, fixingDates2,
payoff, exercise);
engine = new AnalyticDiscreteGeometricAveragePriceAsianEngine(stochProcess);
option3.setPricingEngine(engine);
option4.setPricingEngine(engine);
double price3 = option3.NPV();
double price4 = option4.NPV();
if (Utils.close(price3, price4)) {
Assert.Fail(
"past fixings had no effect on geometric average-price option"
+ "\n without fixings: " + price3
+ "\n with fixings: " + price4);
}
// MC geometric average-price
engine = new MakeMCDiscreteGeometricAPEngine<LowDiscrepancy,Statistics>(stochProcess)
.withStepsPerYear(1)
.withSamples(2047)
.value();
option3.setPricingEngine(engine);
option4.setPricingEngine(engine);
price3 = option3.NPV();
price4 = option4.NPV();
if (Utils.close(price3, price4)) {
Assert.Fail(
"past fixings had no effect on geometric average-price option"
+ "\n without fixings: " + price3
+ "\n with fixings: " + price4);
}
}
public void testMCDiscreteGeometricAveragePrice()
{
//BOOST_MESSAGE("Testing Monte Carlo discrete geometric average-price Asians...");
// data from "Implementing Derivatives Model",
// Clewlow, Strickland, p.118-123
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(100.0);
SimpleQuote qRate = new SimpleQuote(0.03);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.06);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.20);
BlackVolTermStructure volTS =Utilities.flatVol(today, vol, dc);
BlackScholesMertonProcess stochProcess =
new BlackScholesMertonProcess(new Handle<Quote>(spot),
new Handle<YieldTermStructure>(qTS),
new Handle<YieldTermStructure>(rTS),
new Handle<BlackVolTermStructure>(volTS));
double tolerance = 4.0e-3;
IPricingEngine engine =
new MakeMCDiscreteGeometricAPEngine
<LowDiscrepancy,Statistics>(stochProcess)
.withStepsPerYear(1)
.withSamples(8191)
.value();
Average.Type averageType = Average.Type.Geometric;
double runningAccumulator = 1.0;
int pastFixings = 0;
int futureFixings = 10;
Option.Type type = Option.Type.Call;
double strike = 100.0;
StrikedTypePayoff payoff = new PlainVanillaPayoff(type, strike);
Date exerciseDate = today + 360;
Exercise exercise = new EuropeanExercise(exerciseDate);
List<Date> fixingDates = new InitializedList<Date>(futureFixings);
int dt = (int)(360/futureFixings+0.5);
fixingDates[0] = today + dt;
for (int j=1; j<futureFixings; j++)
fixingDates[j] = fixingDates[j-1] + dt;
DiscreteAveragingAsianOption option =
new DiscreteAveragingAsianOption(averageType, runningAccumulator,
pastFixings, fixingDates,
payoff, exercise);
option.setPricingEngine(engine);
double calculated = option.NPV();
IPricingEngine engine2 =
new AnalyticDiscreteGeometricAveragePriceAsianEngine(stochProcess);
option.setPricingEngine(engine2);
double expected = option.NPV();
if (Math.Abs(calculated-expected) > tolerance) {
REPORT_FAILURE("value", averageType, runningAccumulator, pastFixings,
fixingDates, payoff, exercise, spot.value(),
qRate.value(), rRate.value(), today,
vol.value(), expected, calculated, tolerance);
}
}
public void testMCDiscreteArithmeticAverageStrike()
{
//BOOST_MESSAGE("Testing Monte Carlo discrete arithmetic average-strike Asians...");
//QL_TEST_START_TIMING
// data from "Asian Option", Levy, 1997
// in "Exotic Options: The State of the Art",
// edited by Clewlow, Strickland
DiscreteAverageData[] cases5 = {
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 0.0, 11.0/12.0, 2,
0.13, true, 1.51917595129 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 0.0, 11.0/12.0, 4,
0.13, true, 1.67940165674 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 0.0, 11.0/12.0, 8,
0.13, true, 1.75371215251 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 0.0, 11.0/12.0, 12,
0.13, true, 1.77595318693 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 0.0, 11.0/12.0, 26,
0.13, true, 1.81430536630 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 0.0, 11.0/12.0, 52,
0.13, true, 1.82269246898 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 0.0, 11.0/12.0, 100,
0.13, true, 1.83822402464 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 0.0, 11.0/12.0, 250,
0.13, true, 1.83875059026 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 0.0, 11.0/12.0, 500,
0.13, true, 1.83750703638 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 0.0, 11.0/12.0, 1000,
0.13, true, 1.83887181884 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 1.0/12.0, 11.0/12.0, 2,
0.13, true, 1.51154400089 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 1.0/12.0, 11.0/12.0, 4,
0.13, true, 1.67103508506 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 1.0/12.0, 11.0/12.0, 8,
0.13, true, 1.74529684070 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 1.0/12.0, 11.0/12.0, 12,
0.13, true, 1.76667074564 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 1.0/12.0, 11.0/12.0, 26,
0.13, true, 1.80528400613 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 1.0/12.0, 11.0/12.0, 52,
0.13, true, 1.81400883891 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 1.0/12.0, 11.0/12.0, 100,
0.13, true, 1.82922901451 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 1.0/12.0, 11.0/12.0, 250,
0.13, true, 1.82937111773 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 1.0/12.0, 11.0/12.0, 500,
0.13, true, 1.82826193186 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 1.0/12.0, 11.0/12.0, 1000,
0.13, true, 1.82967846654 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 3.0/12.0, 11.0/12.0, 2,
0.13, true, 1.49648170891 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 3.0/12.0, 11.0/12.0, 4,
0.13, true, 1.65443100462 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 3.0/12.0, 11.0/12.0, 8,
0.13, true, 1.72817806731 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 3.0/12.0, 11.0/12.0, 12,
0.13, true, 1.74877367895 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 3.0/12.0, 11.0/12.0, 26,
0.13, true, 1.78733801988 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 3.0/12.0, 11.0/12.0, 52,
0.13, true, 1.79624826757 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 3.0/12.0, 11.0/12.0, 100,
0.13, true, 1.81114186876 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 3.0/12.0, 11.0/12.0, 250,
0.13, true, 1.81101152587 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 3.0/12.0, 11.0/12.0, 500,
0.13, true, 1.81002311939 ),
new DiscreteAverageData(Option.Type.Call, 90.0, 87.0, 0.06, 0.025, 3.0/12.0, 11.0/12.0, 1000,
0.13, true, 1.81145760308 )
};
DayCounter dc = new Actual360();
Date today = Date.Today ;
SimpleQuote spot = new SimpleQuote(100.0);
SimpleQuote qRate = new SimpleQuote(0.03);
YieldTermStructure qTS =Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.06);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.20);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
Average.Type averageType = QLNet.Average.Type.Arithmetic;
double runningSum = 0.0;
int pastFixings = 0;
for (int l=0; l<cases5.Length; l++) {
StrikedTypePayoff payoff =
new PlainVanillaPayoff(cases5[l].type, cases5[l].strike);
double dt = cases5[l].length/(cases5[l].fixings-1);
List<double> timeIncrements = new InitializedList<double>(cases5[l].fixings);
List<Date> fixingDates = new InitializedList<Date>(cases5[l].fixings);
timeIncrements[0] = cases5[l].first;
fixingDates[0] = today + (int)(timeIncrements[0]*360+0.5);
for (int i=1; i<cases5[l].fixings; i++) {
timeIncrements[i] = i*dt + cases5[l].first;
fixingDates[i] = today + (int)(timeIncrements[i]*360+0.5);
}
Exercise exercise = new EuropeanExercise(fixingDates[cases5[l].fixings-1]);
spot.setValue(cases5[l].underlying);
qRate.setValue(cases5[l].dividendYield);
rRate.setValue(cases5[l].riskFreeRate);
vol.setValue(cases5[l].volatility);
BlackScholesMertonProcess stochProcess =
new BlackScholesMertonProcess(new Handle<Quote>(spot),
new Handle<YieldTermStructure>(qTS),
new Handle<YieldTermStructure>(rTS),
new Handle<BlackVolTermStructure>(volTS));
IPricingEngine engine =
new MakeMCDiscreteArithmeticASEngine<LowDiscrepancy,Statistics>(stochProcess)
.withSeed(3456789)
.withSamples(1023)
.value() ;
DiscreteAveragingAsianOption option =
new DiscreteAveragingAsianOption(averageType, runningSum,
pastFixings, fixingDates,
payoff, exercise);
option.setPricingEngine(engine);
double calculated = option.NPV();
double expected = cases5[l].result;
double tolerance = 2.0e-2;
if (Math.Abs(calculated-expected) > tolerance) {
REPORT_FAILURE("value", averageType, runningSum, pastFixings,
fixingDates, payoff, exercise, spot.value(),
qRate.value(), rRate.value(), today,
vol.value(), expected, calculated, tolerance);
}
}
}
public void testMCDiscreteArithmeticAveragePrice()
{
//BOOST_MESSAGE("Testing Monte Carlo discrete arithmetic average-price Asians...");
//QL_TEST_START_TIMING
// data from "Asian Option", Levy, 1997
// in "Exotic Options: The State of the Art",
// edited by Clewlow, Strickland
DiscreteAverageData[] cases4 = {
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 0.0,11.0/12.0, 2,0.13, true, 1.3942835683),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 0.0,11.0/12.0, 4,0.13, true, 1.5852442983),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 0.0,11.0/12.0, 8,0.13, true, 1.66970673),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 0.0,11.0/12.0, 12,0.13, true, 1.6980019214),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 0.0,11.0/12.0, 26,0.13, true, 1.7255070456),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 0.0,11.0/12.0, 52,0.13, true, 1.7401553533),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 0.0,11.0/12.0, 100,0.13, true, 1.7478303712),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 0.0,11.0/12.0, 250,0.13, true, 1.7490291943),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 0.0,11.0/12.0, 500,0.13, true, 1.7515113291),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 0.0,11.0/12.0, 1000,0.13, true, 1.7537344885),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 1.0/12.0,11.0/12.0, 2,0.13, true, 1.8496053697),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 1.0/12.0,11.0/12.0, 4,0.13, true, 2.0111495205),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 1.0/12.0,11.0/12.0, 8,0.13, true, 2.0852138818),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 1.0/12.0,11.0/12.0, 12,0.13, true, 2.1105094397),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 1.0/12.0,11.0/12.0, 26,0.13, true, 2.1346526695),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 1.0/12.0,11.0/12.0, 52,0.13, true, 2.147489651),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 1.0/12.0,11.0/12.0, 100,0.13, true, 2.154728109),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 1.0/12.0,11.0/12.0, 250,0.13, true, 2.1564276565),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 1.0/12.0,11.0/12.0, 500,0.13, true, 2.1594238588),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 1.0/12.0,11.0/12.0, 1000,0.13, true, 2.1595367326),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 3.0/12.0,11.0/12.0, 2,0.13, true, 2.63315092584),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 3.0/12.0,11.0/12.0, 4,0.13, true, 2.76723962361),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 3.0/12.0,11.0/12.0, 8,0.13, true, 2.83124836881),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 3.0/12.0,11.0/12.0, 12,0.13, true, 2.84290301412),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 3.0/12.0,11.0/12.0, 26,0.13, true, 2.88179560417),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 3.0/12.0,11.0/12.0, 52,0.13, true, 2.88447044543),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 3.0/12.0,11.0/12.0, 100,0.13, true, 2.89985329603),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 3.0/12.0,11.0/12.0, 250,0.13, true, 2.90047296063),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 3.0/12.0,11.0/12.0, 500,0.13, true, 2.89813412160),
new DiscreteAverageData(Option.Type.Put, 90.0, 87.0, 0.06, 0.025, 3.0/12.0,11.0/12.0, 1000,0.13, true, 2.89703362437)
};
DayCounter dc = new Actual360();
Date today = Date.Today ;
SimpleQuote spot = new SimpleQuote(100.0);
SimpleQuote qRate = new SimpleQuote(0.03);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.06);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.20);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
Average.Type averageType = Average.Type.Arithmetic;
double runningSum = 0.0;
int pastFixings = 0;
for (int l=0; l<cases4.Length ; l++) {
StrikedTypePayoff payoff = new
PlainVanillaPayoff(cases4[l].type, cases4[l].strike);
double dt = cases4[l].length/(cases4[l].fixings-1);
List<double> timeIncrements = new QLNet.InitializedList<double>(cases4[l].fixings);
List<Date> fixingDates = new QLNet.InitializedList<Date>(cases4[l].fixings);
timeIncrements[0] = cases4[l].first;
fixingDates[0] = today + (int)(timeIncrements[0]*360+0.5);
for (int i=1; i<cases4[l].fixings; i++) {
timeIncrements[i] = i*dt + cases4[l].first;
fixingDates[i] = today + (int)(timeIncrements[i]*360+0.5);
}
Exercise exercise = new EuropeanExercise(fixingDates[cases4[l].fixings-1]);
spot.setValue(cases4[l].underlying);
qRate.setValue(cases4[l].dividendYield);
rRate.setValue(cases4[l].riskFreeRate);
vol.setValue(cases4[l].volatility);
BlackScholesMertonProcess stochProcess =
new BlackScholesMertonProcess(new Handle<Quote>(spot),
new Handle<YieldTermStructure>(qTS),
new Handle<YieldTermStructure>(rTS),
new Handle<BlackVolTermStructure>(volTS));
ulong seed=42;
const int nrTrails = 5000;
LowDiscrepancy.icInstance = new InverseCumulativeNormal();
IRNG rsg = (IRNG)new LowDiscrepancy().make_sequence_generator(nrTrails,seed);
new PseudoRandom().make_sequence_generator(nrTrails,seed);
IPricingEngine engine =
new MakeMCDiscreteArithmeticAPEngine<LowDiscrepancy, Statistics>(stochProcess)
.withStepsPerYear(1)
.withSamples(2047)
.withControlVariate()
.value();
DiscreteAveragingAsianOption option=
new DiscreteAveragingAsianOption(averageType, runningSum,
pastFixings, fixingDates,
payoff, exercise);
option.setPricingEngine(engine);
double calculated = option.NPV();
double expected = cases4[l].result;
double tolerance = 2.0e-2;
if (Math.Abs(calculated-expected) > tolerance) {
REPORT_FAILURE("value", averageType, runningSum, pastFixings,
fixingDates, payoff, exercise, spot.value(),
qRate.value(), rRate.value(), today,
vol.value(), expected, calculated, tolerance);
}
}
}
public void testAnalyticDiscreteGeometricAveragePriceGreeks()
{
//BOOST_MESSAGE("Testing discrete-averaging geometric Asian greeks...");
//SavedSettings backup;
Dictionary<string,double> calculated, expected, tolerance;
calculated = new Dictionary<string, double>(6);
expected = new Dictionary<string, double>(6);
tolerance = new Dictionary<string, double>(6);
tolerance["delta"] = 1.0e-5;
tolerance["gamma"] = 1.0e-5;
tolerance["theta"] = 1.0e-5;
tolerance["rho"] = 1.0e-5;
tolerance["divRho"] = 1.0e-5;
tolerance["vega"] = 1.0e-5;
Option.Type[] types = { Option.Type.Call, Option.Type.Put };
double[] underlyings = { 100.0 };
double[] strikes = { 90.0, 100.0, 110.0 };
double[] qRates = { 0.04, 0.05, 0.06 };
double[] rRates = { 0.01, 0.05, 0.15 };
int[] lengths = { 1, 2 };
double[] vols = { 0.11, 0.50, 1.20 };
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));
BlackScholesMertonProcess process =
new BlackScholesMertonProcess(new Handle<Quote>(spot), qTS, rTS, volTS);
for (int i=0; i<types.Length ; i++) {
for (int j=0; j<strikes.Length ; j++) {
for (int k=0; k<lengths.Length ; k++) {
EuropeanExercise maturity =
new EuropeanExercise(
today + new Period(lengths[k],TimeUnit.Years));
PlainVanillaPayoff payoff =
new PlainVanillaPayoff(types[i], strikes[j]);
double runningAverage = 120;
int pastFixings = 1;
List<Date> fixingDates = new List<Date>();
for (Date d = today + new Period(3, TimeUnit.Months);
d <= maturity.lastDate();
d += new Period(3, TimeUnit.Months))
fixingDates.Add(d);
IPricingEngine engine =
new AnalyticDiscreteGeometricAveragePriceAsianEngine(process);
DiscreteAveragingAsianOption option =
new DiscreteAveragingAsianOption(Average.Type.Geometric,
runningAverage, pastFixings,
fixingDates, payoff, maturity);
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["divRho"] = option.dividendRho();
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 rates and get rho and dividend 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);
double dq = q*1.0e-4;
qRate.setValue(q+dq);
value_p = option.NPV();
qRate.setValue(q-dq);
value_m = option.NPV();
qRate.setValue(q);
expected["divRho"] = (value_p - value_m)/(2*dq);
// 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> kvp in calculated){
string greek = kvp.Key;
double expct = expected[greek],
calcl = calculated[greek],
tol = tolerance [greek];
double error =Utilities.relativeError(expct,calcl,u);
if (error>tol) {
REPORT_FAILURE(greek, Average.Type.Geometric,
runningAverage, pastFixings,
new List<Date>(),
payoff, maturity,
u, q, r, today, v,
expct, calcl, tol);
}
}
}
}
}
}
}
}
}
}
}