void SwingOptionTest::testExtOUJumpVanillaEngine() {
BOOST_TEST_MESSAGE("Testing finite difference pricer for the Kluge model...");
SavedSettings backup;
boost::shared_ptr<ExtOUWithJumpsProcess> jumpProcess = createKlugeProcess();
const Date today = Date::todaysDate();
Settings::instance().evaluationDate() = today;
const DayCounter dc = ActualActual();
const Date maturityDate = today + Period(12, Months);
const Time maturity = dc.yearFraction(today, maturityDate);
const Rate irRate = 0.1;
boost::shared_ptr<YieldTermStructure> rTS(flatRate(today, irRate, dc));
boost::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Call, 30));
boost::shared_ptr<Exercise> exercise(new EuropeanExercise(maturityDate));
boost::shared_ptr<PricingEngine> engine(
new FdExtOUJumpVanillaEngine(jumpProcess, rTS, 25, 200, 50));
VanillaOption option(payoff, exercise);
option.setPricingEngine(engine);
const Real fdNPV = option.NPV();
const Size steps = 100;
const Size nrTrails = 200000;
TimeGrid grid(maturity, steps);
typedef PseudoRandom::rsg_type rsg_type;
typedef MultiPathGenerator<rsg_type>::sample_type sample_type;
rsg_type rsg = PseudoRandom::make_sequence_generator(
jumpProcess->factors()*(grid.size()-1), BigNatural(421));
GeneralStatistics npv;
MultiPathGenerator<rsg_type> generator(jumpProcess, grid, rsg, false);
for (Size n=0; n < nrTrails; ++n) {
sample_type path = generator.next();
const Real x = path.value[0].back();
const Real y = path.value[1].back();
const Real cashflow = (*payoff)(std::exp(x+y));
npv.add(cashflow*rTS->discount(maturity));
}
const Real mcNPV = npv.mean();
const Real mcError = npv.errorEstimate();
if ( std::fabs(fdNPV - mcNPV) > 3.0*mcError) {
BOOST_ERROR("Failed to reproduce FD and MC prices"
<< "\n FD NPV: " << fdNPV
<< "\n MC NPV: " << mcNPV
<< " +/- " << mcError);
}
}
void LiborMarketModelTest::testSwaptionPricing() {
BOOST_TEST_MESSAGE("Testing forward swap and swaption pricing...");
SavedSettings backup;
const Size size = 10;
const Size steps = 8*size;
#if defined(QL_USE_INDEXED_COUPON)
const Real tolerance = 1e-6;
#else
const Real tolerance = 1e-12;
#endif
std::vector<Date> dates;
std::vector<Rate> rates;
dates.push_back(Date(4,September,2005));
dates.push_back(Date(4,September,2011));
rates.push_back(0.04);
rates.push_back(0.08);
boost::shared_ptr<IborIndex> index = makeIndex(dates, rates);
boost::shared_ptr<LiborForwardModelProcess> process(
new LiborForwardModelProcess(size, index));
boost::shared_ptr<LmCorrelationModel> corrModel(
new LmExponentialCorrelationModel(size, 0.5));
boost::shared_ptr<LmVolatilityModel> volaModel(
new LmLinearExponentialVolatilityModel(process->fixingTimes(),
0.291, 1.483, 0.116, 0.00001));
// set-up pricing engine
process->setCovarParam(boost::shared_ptr<LfmCovarianceParameterization>(
new LfmCovarianceProxy(volaModel, corrModel)));
// set-up a small Monte-Carlo simulation to price swations
typedef PseudoRandom::rsg_type rsg_type;
typedef MultiPathGenerator<rsg_type>::sample_type sample_type;
std::vector<Time> tmp = process->fixingTimes();
TimeGrid grid(tmp.begin(), tmp.end(), steps);
Size i;
std::vector<Size> location;
for (i=0; i < tmp.size(); ++i) {
location.push_back(
std::find(grid.begin(),grid.end(),tmp[i])-grid.begin());
}
rsg_type rsg = PseudoRandom::make_sequence_generator(
process->factors()*(grid.size()-1),
BigNatural(42));
const Size nrTrails = 5000;
MultiPathGenerator<rsg_type> generator(process, grid, rsg, false);
boost::shared_ptr<LiborForwardModel>
liborModel(new LiborForwardModel(process, volaModel, corrModel));
Calendar calendar = index->fixingCalendar();
DayCounter dayCounter = index->forwardingTermStructure()->dayCounter();
BusinessDayConvention convention = index->businessDayConvention();
Date settlement = index->forwardingTermStructure()->referenceDate();
boost::shared_ptr<SwaptionVolatilityMatrix> m =
liborModel->getSwaptionVolatilityMatrix();
for (i=1; i < size; ++i) {
for (Size j=1; j <= size-i; ++j) {
Date fwdStart = settlement + Period(6*i, Months);
Date fwdMaturity = fwdStart + Period(6*j, Months);
Schedule schedule(fwdStart, fwdMaturity, index->tenor(), calendar,
convention, convention, DateGeneration::Forward, false);
Rate swapRate = 0.0404;
boost::shared_ptr<VanillaSwap> forwardSwap(
new VanillaSwap(VanillaSwap::Receiver, 1.0,
schedule, swapRate, dayCounter,
schedule, index, 0.0, index->dayCounter()));
forwardSwap->setPricingEngine(boost::shared_ptr<PricingEngine>(
new DiscountingSwapEngine(index->forwardingTermStructure())));
// check forward pricing first
const Real expected = forwardSwap->fairRate();
const Real calculated = liborModel->S_0(i-1,i+j-1);
if (std::fabs(expected - calculated) > tolerance)
BOOST_ERROR("Failed to reproduce fair forward swap rate"
<< "\n calculated: " << calculated
<< "\n expected: " << expected);
swapRate = forwardSwap->fairRate();
forwardSwap = boost::shared_ptr<VanillaSwap>(
new VanillaSwap(VanillaSwap::Receiver, 1.0,
schedule, swapRate, dayCounter,
schedule, index, 0.0, index->dayCounter()));
forwardSwap->setPricingEngine(boost::shared_ptr<PricingEngine>(
new DiscountingSwapEngine(index->forwardingTermStructure())));
if (i == j && i<=size/2) {
boost::shared_ptr<PricingEngine> engine(
new LfmSwaptionEngine(liborModel,
index->forwardingTermStructure()));
boost::shared_ptr<Exercise> exercise(
new EuropeanExercise(process->fixingDates()[i]));
boost::shared_ptr<Swaption> swaption(
new Swaption(forwardSwap, exercise));
swaption->setPricingEngine(engine);
GeneralStatistics stat;
for (Size n=0; n<nrTrails; ++n) {
sample_type path = (n%2) ? generator.antithetic()
: generator.next();
std::vector<Rate> rates(size);
for (Size k=0; k<process->size(); ++k) {
rates[k] = path.value[k][location[i]];
}
std::vector<DiscountFactor> dis =
process->discountBond(rates);
Real npv=0.0;
for (Size m=i; m < i+j; ++m) {
npv += (swapRate - rates[m])
* ( process->accrualEndTimes()[m]
- process->accrualStartTimes()[m])*dis[m];
}
stat.add(std::max(npv, 0.0));
}
if (std::fabs(swaption->NPV() - stat.mean())
> stat.errorEstimate()*2.35)
BOOST_ERROR("Failed to reproduce swaption npv"
<< "\n calculated: " << stat.mean()
<< "\n expected: " << swaption->NPV());
}
}
}
}
void VPPTest::testVPPPricing() {
BOOST_TEST_MESSAGE("Testing VPP pricing using perfect foresight or FDM...");
SavedSettings backup;
const Date today = Date(18, December, 2011);
const DayCounter dc = ActualActual();
Settings::instance().evaluationDate() = today;
// vpp paramter
const Real heatRate = 2.5;
const Real pMin = 8;
const Real pMax = 40;
const Size tMinUp = 6;
const Size tMinDown = 2;
const Real startUpFuel = 20;
const Real startUpFixCost = 100;
const boost::shared_ptr<SwingExercise> exercise(
new SwingExercise(today, today+6, 3600u));
VanillaVPPOption vppOption(heatRate, pMin, pMax, tMinUp, tMinDown,
startUpFuel, startUpFixCost, exercise);
const boost::shared_ptr<KlugeExtOUProcess> klugeOUProcess
= createKlugeExtOUProcess();
const boost::shared_ptr<ExtOUWithJumpsProcess> lnPowerProcess
= klugeOUProcess->getKlugeProcess();
const boost::shared_ptr<ExtendedOrnsteinUhlenbeckProcess> ouProcess
= lnPowerProcess->getExtendedOrnsteinUhlenbeckProcess();
const boost::shared_ptr<ExtendedOrnsteinUhlenbeckProcess> lnGasProcess
= klugeOUProcess->getExtOUProcess();
const Real beta = lnPowerProcess->beta();
const Real eta = lnPowerProcess->eta();
const Real lambda = lnPowerProcess->jumpIntensity();
const Real alpha = ouProcess->speed();
const Real volatility_x = ouProcess->volatility();
const Real kappa = lnGasProcess->speed();
const Real volatility_u = lnGasProcess->volatility();
const Rate irRate = 0.00;
const Real fuelCostAddon = 3.0;
const boost::shared_ptr<YieldTermStructure> rTS
= flatRate(today, irRate, dc);
const Size nHours = LENGTH(powerPrices);
typedef FdSimpleKlugeExtOUVPPEngine::Shape Shape;
boost::shared_ptr<Shape> fuelShape(new Shape(nHours));
boost::shared_ptr<Shape> powerShape(new Shape(nHours));
for (Size i=0; i < nHours; ++i) {
const Time t = (i+1)/(365*24.);
const Real fuelPrice = fuelPrices[i];
const Real gs = std::log(fuelPrice)-square<Real>()(volatility_u)
/(4*kappa)*(1-std::exp(-2*kappa*t));
(*fuelShape)[i] = Shape::value_type(t, gs);
const Real powerPrice = powerPrices[i];
const Real ps = std::log(powerPrice)-square<Real>()(volatility_x)
/(4*alpha)*(1-std::exp(-2*alpha*t))
-lambda/beta*std::log((eta-std::exp(-beta*t))/(eta-1.0));
(*powerShape)[i] = Shape::value_type(t, ps);
}
// Test: intrinsic value
vppOption.setPricingEngine(boost::shared_ptr<PricingEngine>(
new DynProgVPPIntrinsicValueEngine(
std::vector<Real>(fuelPrices, fuelPrices+nHours),
std::vector<Real>(powerPrices, powerPrices+nHours),
fuelCostAddon, flatRate(0.0, dc))));
const Real intrinsic = vppOption.NPV();
const Real expectedIntrinsic = 2056.04;
if (std::fabs(intrinsic - expectedIntrinsic) > 0.1) {
BOOST_ERROR("Failed to reproduce intrinsic value"
<< "\n calculated: " << intrinsic
<< "\n expected : " << expectedIntrinsic);
}
// Test: finite difference price
const boost::shared_ptr<PricingEngine> engine(
new FdSimpleKlugeExtOUVPPEngine(klugeOUProcess, rTS,
fuelShape, powerShape, fuelCostAddon,
1, 25, 11, 10));
vppOption.setPricingEngine(engine);
const Real fdmPrice = vppOption.NPV();
const Real expectedFdmPrice = 5217.68;
if (std::fabs(fdmPrice - expectedFdmPrice) > 0.1) {
BOOST_ERROR("Failed to reproduce finite difference price"
<< "\n calculated: " << fdmPrice
<< "\n expected : " << expectedFdmPrice);
}
// Test: Monte-Carlo perfect foresight price
VanillaVPPOption::arguments args;
vppOption.setupArguments(&args);
const FdmVPPStepConditionFactory stepConditionFactory(args);
const boost::shared_ptr<FdmMesher> oneDimMesher(new FdmMesherComposite(
stepConditionFactory.stateMesher()));
const Size nStates = oneDimMesher->layout()->dim()[0];
const FdmVPPStepConditionMesher vppMesh = { 0u, oneDimMesher };
const TimeGrid grid(dc.yearFraction(today, exercise->lastDate()+1),
exercise->dates().size());
typedef PseudoRandom::rsg_type rsg_type;
typedef MultiPathGenerator<rsg_type>::sample_type sample_type;
rsg_type rsg = PseudoRandom::make_sequence_generator(
klugeOUProcess->factors()*(grid.size()-1), 1234ul);
MultiPathGenerator<rsg_type> generator(klugeOUProcess, grid, rsg, false);
GeneralStatistics npv;
const Size nTrails = 2500;
for (Size i=0; i < nTrails; ++i) {
const sample_type& path = generator.next();
const boost::shared_ptr<FdmVPPStepCondition> stepCondition(
stepConditionFactory.build(
vppMesh, fuelCostAddon,
boost::shared_ptr<FdmInnerValueCalculator>(
new PathFuelPrice(path.value, fuelShape)),
boost::shared_ptr<FdmInnerValueCalculator>(
new PathSparkSpreadPrice(heatRate, path.value,
fuelShape, powerShape))));
Array state(nStates, 0.0);
for (Size j=exercise->dates().size(); j > 0; --j) {
stepCondition->applyTo(state, grid.at(j));
state*=rTS->discount(grid.at(j))/rTS->discount(grid.at(j-1));
}
npv.add(state.back());
}
Real npvMC = npv.mean();
Real errorMC = npv.errorEstimate();
const Real expectedMC = 5250.0;
if (std::fabs(npvMC-expectedMC) > 3*errorMC) {
BOOST_ERROR("Failed to reproduce Monte-Carlo price"
<< "\n calculated: " << npvMC
<< "\n error ; " << errorMC
<< "\n expected : " << expectedMC);
}
npv.reset();
// Test: Longstaff Schwartz least square Monte-Carlo
const Size nCalibrationTrails = 1000u;
std::vector<sample_type> calibrationPaths;
std::vector<boost::shared_ptr<FdmVPPStepCondition> > stepConditions;
std::vector<boost::shared_ptr<FdmInnerValueCalculator> > sparkSpreads;
sparkSpreads.reserve(nCalibrationTrails);
stepConditions.reserve(nCalibrationTrails);
calibrationPaths.reserve(nCalibrationTrails);
for (Size i=0; i < nCalibrationTrails; ++i) {
calibrationPaths.push_back(generator.next());
sparkSpreads.push_back(boost::shared_ptr<FdmInnerValueCalculator>(
new PathSparkSpreadPrice(heatRate, calibrationPaths.back().value,
fuelShape, powerShape)));
stepConditions.push_back(stepConditionFactory.build(
vppMesh, fuelCostAddon,
boost::shared_ptr<FdmInnerValueCalculator>(
new PathFuelPrice(calibrationPaths.back().value, fuelShape)),
sparkSpreads.back()));
}
const FdmLinearOpIterator iter = oneDimMesher->layout()->begin();
// prices of all calibration paths for all states
std::vector<Array> prices(nCalibrationTrails, Array(nStates, 0.0));
// regression coefficients for all states and all exercise dates
std::vector<std::vector<Array> > coeff(
nStates, std::vector<Array>(exercise->dates().size(), Array()));
// regression functions
const Size dim = 1u;
std::vector<boost::function1<Real, Array> > v(
LsmBasisSystem::multiPathBasisSystem(dim,5u, LsmBasisSystem::Monomial));
for (Size i=exercise->dates().size(); i > 0u; --i) {
const Time t = grid.at(i);
std::vector<Array> x(nCalibrationTrails, Array(dim));
for (Size j=0; j < nCalibrationTrails; ++j) {
x[j][0] = sparkSpreads[j]->innerValue(iter, t);
}
for (Size k=0; k < nStates; ++k) {
std::vector<Real> y(nCalibrationTrails);
for (Size j=0; j < nCalibrationTrails; ++j) {
y[j] = prices[j][k];
}
coeff[k][i-1] = GeneralLinearLeastSquares(x, y, v).coefficients();
for (Size j=0; j < nCalibrationTrails; ++j) {
prices[j][k] = 0.0;
for (Size l=0; l < v.size(); ++l) {
prices[j][k] += coeff[k][i-1][l]*v[l](x[j]);
}
}
}
for (Size j=0; j < nCalibrationTrails; ++j) {
stepConditions[j]->applyTo(prices[j], grid.at(i));
}
}
Real tmpValue = 0.0;
for (Size i=0; i < nTrails; ++i) {
Array x(dim), state(nStates, 0.0), contState(nStates, 0.0);
const sample_type& path = (i % 2) ? generator.antithetic()
: generator.next();
const boost::shared_ptr<FdmInnerValueCalculator> fuelPrices(
new PathFuelPrice(path.value, fuelShape));
const boost::shared_ptr<FdmInnerValueCalculator> sparkSpreads(
new PathSparkSpreadPrice(heatRate, path.value,
fuelShape, powerShape));
for (Size j=exercise->dates().size(); j > 0u; --j) {
const Time t = grid.at(j);
const Real fuelPrice = fuelPrices->innerValue(iter, t);
const Real sparkSpread = sparkSpreads->innerValue(iter, t);
const Real startUpCost
= startUpFixCost + (fuelPrice + fuelCostAddon)*startUpFuel;
x[0] = sparkSpread;
for (Size k=0; k < nStates; ++k) {
contState[k] = 0.0;
for (Size l=0; l < v.size(); ++l) {
contState[k] += coeff[k][j-1][l]*v[l](x);
}
}
const Real pMinFlow = pMin*(sparkSpread - heatRate*fuelCostAddon);
const Real pMaxFlow = pMax*(sparkSpread - heatRate*fuelCostAddon);
// rollback continuation states and the path states
for (Size i=0; i < 2*tMinUp; ++i) {
if (i < tMinUp) {
state[i] += pMinFlow;
contState[i]+= pMinFlow;
}
else {
state[i] += pMaxFlow;
contState[i]+= pMaxFlow;
}
}
// dynamic programming using the continuation values
Array retVal(nStates);
for (Size i=0; i < tMinUp-1; ++i) {
retVal[i] = retVal[tMinUp + i]
= (contState[i+1] > contState[tMinUp + i+1])?
state[i+1] : state[tMinUp + i+1];
}
if (contState[2*tMinUp] >=
std::max(contState[tMinUp-1], contState[2*tMinUp-1])) {
retVal[tMinUp-1] = retVal[2*tMinUp-1] = state[2*tMinUp];
}
else if (contState[tMinUp-1] >= contState[2*tMinUp-1]) {
retVal[tMinUp-1] = retVal[2*tMinUp-1] = state[tMinUp-1];
}
else {
retVal[tMinUp-1] = retVal[2*tMinUp-1] = state[2*tMinUp-1];
}
for (Size i=0; i < tMinDown-1; ++i) {
retVal[2*tMinUp + i] = state[2*tMinUp + i+1];
}
if (contState.back() >=
std::max(contState.front(), contState[tMinUp]) - startUpCost) {
retVal.back() = state.back();
}
else if (contState.front() > contState[tMinUp]) {
retVal.back() = state.front()-startUpCost;
}
else {
retVal.back() = state[tMinUp]-startUpCost;
}
state = retVal;
}
tmpValue+=0.5*state.back();
if ((i%2)) {
npv.add(tmpValue, 1.0);
tmpValue = 0.0;
}
}
npvMC = npv.mean();
errorMC = npv.errorEstimate();
if (std::fabs(npvMC-fdmPrice) > 3*errorMC) {
BOOST_ERROR("Failed to reproduce Least Square Monte-Carlo price"
<< "\n calculated : " << npvMC
<< "\n error : " << errorMC
<< "\n expected FDM : " << fdmPrice);
}
}
void VPPTest::testKlugeExtOUSpreadOption() {
BOOST_TEST_MESSAGE("Testing Simple Kluge ext-Ornstein-Uhlenbeck spread option...");
SavedSettings backup;
Date settlementDate = Date(18, December, 2011);
Settings::instance().evaluationDate() = settlementDate;
DayCounter dayCounter = ActualActual();
Date maturityDate = settlementDate + Period(1, Years);
Time maturity = dayCounter.yearFraction(settlementDate, maturityDate);
const Real speed = 1.0;
const Volatility vol = std::sqrt(1.4);
const Real betaG = 0.0;
const Real alphaG = 3.0;
const Real x0G = 3.0;
const Rate irRate = 0.0;
const Real heatRate = 2.0;
const Real rho = 0.5;
boost::shared_ptr<ExtOUWithJumpsProcess>
klugeProcess = createKlugeProcess();
boost::function<Real (Real)> f = alphaG + betaG*boost::lambda::_1;
boost::shared_ptr<ExtendedOrnsteinUhlenbeckProcess> extOUProcess(
new ExtendedOrnsteinUhlenbeckProcess(speed, vol, x0G, f,
ExtendedOrnsteinUhlenbeckProcess::Trapezodial));
boost::shared_ptr<YieldTermStructure> rTS(
flatRate(settlementDate, irRate, dayCounter));
boost::shared_ptr<KlugeExtOUProcess> klugeOUProcess(
new KlugeExtOUProcess(rho, klugeProcess, extOUProcess));
boost::shared_ptr<Payoff> payoff(new PlainVanillaPayoff(Option::Call, 0.0));
Array spreadFactors(2);
spreadFactors[0] = 1.0; spreadFactors[1] = -heatRate;
boost::shared_ptr<BasketPayoff> basketPayoff(
new AverageBasketPayoff(payoff, spreadFactors));
boost::shared_ptr<Exercise> exercise(new EuropeanExercise(maturityDate));
BasketOption option(basketPayoff, exercise);
option.setPricingEngine(boost::shared_ptr<PricingEngine>(
new FdKlugeExtOUSpreadEngine(klugeOUProcess, rTS,
5, 200, 50, 20)));
TimeGrid grid(maturity, 50);
typedef PseudoRandom::rsg_type rsg_type;
typedef MultiPathGenerator<rsg_type>::sample_type sample_type;
rsg_type rsg = PseudoRandom::make_sequence_generator(
klugeOUProcess->factors()*(grid.size()-1), 1234ul);
MultiPathGenerator<rsg_type> generator(klugeOUProcess, grid, rsg, false);
GeneralStatistics npv;
const Size nTrails = 20000;
for (Size i=0; i < nTrails; ++i) {
const sample_type path = generator.next();
Array p(2);
p[0] = path.value[0].back() + path.value[1].back();
p[1] = path.value[2].back();
npv.add((*basketPayoff)(Exp(p)));
}
const Real calculated = option.NPV();
const Real expectedMC = npv.mean();
const Real mcError = npv.errorEstimate();
if (std::fabs(expectedMC - calculated) > 3*mcError) {
BOOST_ERROR("Failed to reproduce referenc values"
<< "\n calculated: " << calculated
<< "\n expected(MC): " << expectedMC
<< "\n mc error : " << mcError);
}
}
CatBond::results MonteCarloCatBondEngine::npv(bool includeSettlementDateFlows,
Date settlementDate,
Date npvDate) const
{
const size_t MAX_PATHS = 10000; //TODO
CatBond::results result;
result.reset();
double lossProbability = 0.0;
double exhaustionProbability = 0.0;
double expectedLoss = 0.0;
//GenericRiskStatistics<GeneralStatistics> statistics;
GeneralStatistics statistics;
if (arguments_.cashflows.empty()) {
return result;
}
if (settlementDate == Date())
settlementDate = Settings::instance().evaluationDate();
if (npvDate == Date())
npvDate = settlementDate;
Real totalNPV = 0.0;
Date effectiveDate = std::max(arguments_.startDate, settlementDate);
Date maturityDate = (*arguments_.cashflows.rbegin())->date();
auto catSimulation = catRisk_->newSimulation(effectiveDate, maturityDate);
std::vector<std::pair<Date, Real> > eventsPath;
NotionalPath notionalPath;
Real riskFreeNPV = pathNpv(includeSettlementDateFlows, settlementDate, notionalPath);
size_t pathCount=0;
while(catSimulation->nextPath(eventsPath) && pathCount<MAX_PATHS)
{
arguments_.notionalRisk->updatePath(eventsPath, notionalPath);
if(notionalPath.loss()>0) { //optimization, most paths will not include any loss
double thisNpv = pathNpv(includeSettlementDateFlows, settlementDate, notionalPath);
totalNPV += thisNpv;
lossProbability+=1;
if (notionalPath.loss()==1)
exhaustionProbability+=1;
expectedLoss+=notionalPath.loss();
statistics.add(thisNpv, 1.0);
} else {
totalNPV += riskFreeNPV;
statistics.add(riskFreeNPV, 1.0);
}
pathCount++;
}
lossProbability/=pathCount;
exhaustionProbability/=pathCount;
expectedLoss/=pathCount;
result.valuationDate = settlementDate;
result.value = totalNPV/(pathCount*discountCurve_->discount(npvDate));
result.settlementValue = result.value;
result.lossProbability = lossProbability;
result.exhaustionProbability = exhaustionProbability;
result.expectedLoss = expectedLoss;
if(Null<Real>()!=varLevel_) {
result.var = result.value - statistics.percentile(1.0-varLevel_);
result.stdDev = statistics.standardDeviation();
result.skew = statistics.skewness();
result.kurtosis = statistics.kurtosis();
}
return result;
}
void SwingOptionTest::testExtOUJumpSwingOption() {
BOOST_TEST_MESSAGE("Testing simple swing option pricing for Kluge model...");
SavedSettings backup;
Date settlementDate = Date::todaysDate();
Settings::instance().evaluationDate() = settlementDate;
DayCounter dayCounter = ActualActual();
Date maturityDate = settlementDate + Period(12, Months);
boost::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Put, 30));
std::vector<Date> exerciseDates(1, settlementDate+Period(1, Months));
while (exerciseDates.back() < maturityDate) {
exerciseDates.push_back(exerciseDates.back()+Period(1, Months));
}
boost::shared_ptr<SwingExercise> swingExercise(
new SwingExercise(exerciseDates));
std::vector<Time> exerciseTimes(exerciseDates.size());
for (Size i=0; i < exerciseTimes.size(); ++i) {
exerciseTimes[i]
= dayCounter.yearFraction(settlementDate, exerciseDates[i]);
}
TimeGrid grid(exerciseTimes.begin(), exerciseTimes.end(), 60);
std::vector<Size> exerciseIndex(exerciseDates.size());
for (Size i=0; i < exerciseIndex.size(); ++i) {
exerciseIndex[i] = grid.closestIndex(exerciseTimes[i]);
}
boost::shared_ptr<ExtOUWithJumpsProcess> jumpProcess = createKlugeProcess();
const Rate irRate = 0.1;
boost::shared_ptr<YieldTermStructure> rTS(
flatRate(settlementDate, irRate, dayCounter));
boost::shared_ptr<PricingEngine> swingEngine(
new FdSimpleExtOUJumpSwingEngine(jumpProcess, rTS, 25, 50, 25));
boost::shared_ptr<PricingEngine> vanillaEngine(
new FdExtOUJumpVanillaEngine(jumpProcess, rTS, 25, 50, 25));
VanillaOption bermudanOption(payoff, swingExercise);
bermudanOption.setPricingEngine(vanillaEngine);
const Real bermudanOptionPrices = bermudanOption.NPV();
const Size nrTrails = 16000;
typedef PseudoRandom::rsg_type rsg_type;
typedef MultiPathGenerator<rsg_type>::sample_type sample_type;
rsg_type rsg = PseudoRandom::make_sequence_generator(
jumpProcess->factors()*(grid.size()-1), BigNatural(421));
MultiPathGenerator<rsg_type> generator(jumpProcess, grid, rsg, false);
for (Size i=0; i < exerciseDates.size(); ++i) {
const Size exerciseRights = i+1;
VanillaSwingOption swingOption(payoff, swingExercise,
exerciseRights, exerciseRights);
swingOption.setPricingEngine(swingEngine);
const Real swingOptionPrice = swingOption.NPV();
const Real upperBound = exerciseRights*bermudanOptionPrices;
if (swingOptionPrice - upperBound > 2e-2) {
BOOST_ERROR("Failed to reproduce upper bounds"
<< "\n upper Bound: " << upperBound
<< "\n Price: " << swingOptionPrice);
}
Real lowerBound = 0.0;
for (Size j=exerciseDates.size()-i-1; j < exerciseDates.size(); ++j) {
VanillaOption europeanOption(payoff, boost::shared_ptr<Exercise>(
new EuropeanExercise(exerciseDates[j])));
europeanOption.setPricingEngine(
boost::shared_ptr<PricingEngine>(vanillaEngine));
lowerBound += europeanOption.NPV();
}
if (lowerBound - swingOptionPrice > 2e-2) {
BOOST_ERROR("Failed to reproduce lower bounds"
<< "\n lower Bound: " << lowerBound
<< "\n Price: " << swingOptionPrice);
}
// use MC plus perfect forecast to find an upper bound
GeneralStatistics npv;
for (Size n=0; n < nrTrails; ++n) {
sample_type path = generator.next();
std::vector<Real> exerciseValues(exerciseTimes.size());
for (Size k=0; k < exerciseTimes.size(); ++k) {
const Real x = path.value[0][exerciseIndex[k]];
const Real y = path.value[1][exerciseIndex[k]];
const Real s = std::exp(x+y);
exerciseValues[k] =(*payoff)(s)*rTS->discount(exerciseDates[k]);
}
std::sort(exerciseValues.begin(), exerciseValues.end(),
std::greater<Real>());
Real npCashFlows
= std::accumulate(exerciseValues.begin(),
exerciseValues.begin()+exerciseRights, 0.0);
npv.add(npCashFlows);
}
const Real mcUpperBound = npv.mean();
const Real mcErrorUpperBound = npv.errorEstimate();
if (swingOptionPrice - mcUpperBound > 2.36*mcErrorUpperBound) {
BOOST_ERROR("Failed to reproduce mc upper bounds"
<< "\n mc upper Bound: " << mcUpperBound
<< "\n Price: " << swingOptionPrice);
}
}
}
