void StatisticsTest::testIncrementalStatistics() {
BOOST_TEST_MESSAGE("Testing incremental statistics...");
// With QuantLib 1.7 IncrementalStatistics was changed to
// a wrapper to the boost accumulator library. This is
// a test of the new implementation against results from
// the old one.
MersenneTwisterUniformRng mt(42);
IncrementalStatistics stat;
for (Size i = 0; i < 500000; ++i) {
Real x = 2.0 * (mt.nextReal() - 0.5) * 1234.0;
Real w = mt.nextReal();
stat.add(x, w);
}
TEST_INC_STAT(stat.samples(), 500000);
TEST_INC_STAT(stat.weightSum(), 2.5003623600676749e+05);
TEST_INC_STAT(stat.mean(), 4.9122325964293845e-01);
TEST_INC_STAT(stat.variance(), 5.0706503959683329e+05);
TEST_INC_STAT(stat.standardDeviation(), 7.1208499464378076e+02);
TEST_INC_STAT(stat.errorEstimate(), 1.0070402569876076e+00);
TEST_INC_STAT(stat.skewness(), -1.7360169326720038e-03);
TEST_INC_STAT(stat.kurtosis(), -1.1990742562085395e+00);
TEST_INC_STAT(stat.min(), -1.2339945045639761e+03);
TEST_INC_STAT(stat.max(), 1.2339958308008499e+03);
TEST_INC_STAT(stat.downsideVariance(), 5.0786776146975247e+05);
TEST_INC_STAT(stat.downsideDeviation(), 7.1264841364431061e+02);
// This is a test for numerical stability,
// where the old implementation fails
InverseCumulativeRng<MersenneTwisterUniformRng,InverseCumulativeNormal> normal_gen(mt);
IncrementalStatistics stat2;
for (Size i = 0; i < 500000; ++i) {
Real x = normal_gen.next().value * 1E-1 + 1E8;
Real w = 1.0;
stat2.add(x, w);
}
Real tol = 1E-5;
if(std::fabs( stat2.variance() - 1E-2 ) > tol)
BOOST_ERROR("variance (" << stat2.variance()
<< ") out of expected range " << 1E-2 << " +- "
<< tol);
}
// evaluate fitting error on benchmark with parameter set
Real HestonPriceBenchmark(Handle<Quote> &s0, std::vector<CALIB> &c, std::vector<RD> &rd,
std::vector<double> p, double sdCutOff) {
Date settlementDate(24, January, 2011);
SavedSettings backup;
Settings::instance().evaluationDate() = settlementDate;
Real theta = p[0];
Real kappa = p[1];
Real sigma = p[2];
Real rho = p[3];
Real v0 = p[4];
std::cout << "Theta: " << theta <<
"\nKappa: " << kappa <<
"\nsigma: " << sigma <<
"\nrho: " << rho <<
"\nv0: " << v0 << std::endl;
DayCounter dayCounter = Actual365Fixed();
Calendar calendar = TARGET();
std::vector<Date> dates;
std::vector<Rate> rates;
std::vector<Rate> div;
// this is indispensable: expiry in Heston helper is computed from YC settlement date
dates.push_back(settlementDate);
rates.push_back(rd[0].R);
div.push_back(rd[0].D);
for (Size i = 0; i < rd.size(); ++i) {
Integer days = 365*rd[i].T;
dates.push_back(settlementDate + days);
rates.push_back(rd[i].R);
div.push_back(rd[i].D);
}
Date dtLast = settlementDate + ((int) 365*rd[rd.size()-1].T);
std::cout << "Last curve date: " << dtLast << std::endl;
Integer days = (rd[rd.size()-1].T+1)*365;
dates.push_back(settlementDate + days);
rates.push_back(rd[rd.size()-1].R);
div.push_back(rd[rd.size()-1].D);
std::cout << "Heston model Benchmark Pricing: TS..." << std::endl;
Handle<YieldTermStructure> riskFreeTS(
boost::shared_ptr<YieldTermStructure>(
new ZeroCurve(dates, rates, dayCounter)));
Handle<YieldTermStructure> dividendTS(
boost::shared_ptr<YieldTermStructure>(
new ZeroCurve(dates, div, dayCounter)));
Volatility vol = 2.0;
Handle<BlackVolTermStructure> volTS(
boost::shared_ptr<BlackVolTermStructure>(
new BlackConstantVol(settlementDate, calendar, vol,
dayCounter)));
boost::shared_ptr<BlackScholesMertonProcess> BSprocess(
new BlackScholesMertonProcess(s0, dividendTS, riskFreeTS, volTS));
// boost::shared_ptr<PricingEngine> BSengine(
// new AnalyticEuropeanEngine(BSprocess));
boost::shared_ptr<HestonProcess> process(new HestonProcess(
riskFreeTS, dividendTS, s0, v0, kappa, theta, sigma, rho));
boost::shared_ptr<PricingEngine> engine(new AnalyticHestonEngine(
boost::shared_ptr<HestonModel>(new HestonModel(process)), 64));
std::cout << "Heston model Benchmark Pricing: engine set ..." << std::endl;
IncrementalStatistics errorStat;
vector<Real> error;
ofstream myfile;
Volatility ivol;
Real errorBid;
Real errorAsk;
// myfile.open ("dump.csv", ios::out|ios::trunc); // this is the default
// myfile << "T, dm, y, CP, PB, Calc, PA, Vega, iVol, ErrorBid, ErrorAsk" << std::endl;
for (Size i = 0; i < c.size(); ++i) {
Integer days = 365*c[i].T;
//std::cout << "Expiry dates: " << dtExpiry << std::endl;
Period maturity((int)((days+3)/7.), Weeks); // round to weeks
Date dtExpiry = calendar.advance(riskFreeTS->referenceDate(),
maturity);
if (i==0)
std::cout << dtExpiry << std::endl;
// Time tau = riskFreeTS->dayCounter().yearFraction(
// riskFreeTS->referenceDate(), dtExpiry);
boost::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Call, c[i].K));
boost::shared_ptr<Exercise> exercise(new EuropeanExercise(dtExpiry));
VanillaOption option(payoff, exercise);
option.setPricingEngine(engine);
Real calculated = option.NPV();
// option.setPricingEngine(BSengine);
if (calculated >0) {
try {
ivol = option.impliedVolatility(calculated, BSprocess, 1.e-6, 1000, .1, 10);
errorBid = std::max((c[i].VB-ivol), 0.0)*100;
errorAsk = std::max((ivol-c[i].VA), 0.0)*100;
} catch (...) {
errorBid = 0.0;
errorAsk = 0.0;
};
} else {
vol = 0.0;
errorAsk = 0.0;
errorBid = 0.0;
};
error.push_back(errorBid+errorAsk);
// myfile << c[i].T << "," << dtExpiry << "," << c[i].CP << "," << c[i].PB << "," << calculated << "," << c[i].PA << "," << c[i].Vega << "," << ivol << "," << errorBid << "," << errorAsk << std::endl;
}
// remove outliers and calculate sse
errorStat.addSequence(error.begin(), error.end());
Real sse = errorStat.standardDeviation();
for (Size i=0; i<error.size(); ++i)
if (abs(error[i]) > sdCutOff*sse) error[i] = 0.0;
errorStat.reset();
errorStat.addSequence(error.begin(), error.end());
sse = errorStat.standardDeviation();
return sse;
}
