PathGeneratorFactory::PathGeneratorFactory(const boost::shared_ptr<StochasticProcessArray>& processes,
const TimeGrid& timeGrid)
: processes_(processes), grid_(timeGrid)
{
unsigned long myseed = static_cast<unsigned long>(1);
rand_ = std::tr1::mt19937(myseed);
this->numAssets_ = processes->size();
this->pathSize_ = timeGrid.size();
PseudoRandom::rsg_type gen =
PseudoRandom::make_sequence_generator(numAssets_*(timeGrid.size()-1),1);
gen_ = boost::shared_ptr<MultiVariate<PseudoRandom>::path_generator_type>(new MultiVariate<PseudoRandom>::path_generator_type(processes,
timeGrid, gen, false));
this->next_ = MultiPath(numAssets_,this->grid_);
S0_ = std::valarray<double>(numAssets_);
randArrs_ = std::valarray<double>(numAssets_);
//this->testRandom_ = Array(numAssets_ * pathSize_);
previousRand_ = Matrix(numAssets_, pathSize_);
Matrix corr = processes->correlation();
chol_=CholeskyDecomposition(corr);
random_ = MultiPath(numAssets_,timeGrid);
// num - 1
this->muGrid_ = Matrix(numAssets_, timeGrid.size() - 1);
this->volGrid_ = Matrix(numAssets_,timeGrid.size() - 1);
antitheticFlag_ = false;
for (Size asset = 0 ; asset<numAssets_ ;++asset)
{
//초기화 수익률 or 절대값
S0_[asset] = processes->process(asset)->x0() / processes->process(asset)->basePrice();
for (Size t = 0 ; t < pathSize_ - 1 ;++t)
{
double mu_t = processes->process(asset)->drift(timeGrid[t],1.0);
double sigma_t = processes->process(asset)->diffusion(timeGrid[t],1.0);
double dt_t = timeGrid.dt(t);
// exp( ( mu[t] - 0.5 * vol[t] * vol[t] ) * dt[t] )
muGrid_[asset][t] = std::exp( ( mu_t - 0.5 * sigma_t * sigma_t ) * dt_t );
// vol[t] * sqrt(dt[t])
volGrid_[asset][t] = sigma_t * std::sqrt(dt_t);
}
}
}
boost::shared_ptr<Lattice> HullWhite::tree(const TimeGrid& grid) const {
TermStructureFittingParameter phi(termStructure());
boost::shared_ptr<ShortRateDynamics> numericDynamics(
new Dynamics(phi, a(), sigma()));
boost::shared_ptr<TrinomialTree> trinomial(
new TrinomialTree(numericDynamics->process(), grid));
boost::shared_ptr<ShortRateTree> numericTree(
new ShortRateTree(trinomial, numericDynamics, grid));
typedef TermStructureFittingParameter::NumericalImpl NumericalImpl;
boost::shared_ptr<NumericalImpl> impl =
boost::dynamic_pointer_cast<NumericalImpl>(phi.implementation());
impl->reset();
for (Size i=0; i<(grid.size() - 1); i++) {
Real discountBond = termStructure()->discount(grid[i+1]);
const Array& statePrices = numericTree->statePrices(i);
Size size = numericTree->size(i);
Time dt = numericTree->timeGrid().dt(i);
Real dx = trinomial->dx(i);
Real x = trinomial->underlying(i,0);
Real value = 0.0;
for (Size j=0; j<size; j++) {
value += statePrices[j]*std::exp(-x*dt);
x += dx;
}
value = std::log(value/discountBond)/dt;
impl->set(grid[i], value);
}
return numericTree;
}
boost::shared_ptr<path_generator_type> pathGenerator() const {
Size numAssets = processes_->size();
TimeGrid grid = timeGrid();
Calendar calendar = this->arguments_.sp_payoff->calendar();
typename RNG::rsg_type gen =
RNG::make_sequence_generator(numAssets*(grid.size()-1),seed_);
boost::shared_ptr<path_generator_type> pgPtr
= boost::shared_ptr<path_generator_type>(
new path_generator_type(processes_,
grid,
gen));
PathInformation::instance().initialize(pgPtr->multiPath(),calendar);
//history setting here..
//index의 Calendar와 product의 Calendar(calculation Date Calendar)는 따로 가야함
//과거 index fixing은 각각 클래스에서 fixing하는데 그 방법은 pathmanager가 indexHistory를 가지고 있어서 거기에 문의해서,
//따로 클래스 내에 가져와서 fixing 시켜놈. 결과만 저장해서 나중에 함침.
//그러므로 path에 따로 무언가를 붙일 필요는 없음.
//MultiPath Grid는 product calendar로 grid숫자 계산함.
return pgPtr;
}
//! Return shared pointer to path generator who generates sample pathes in simulation
virtual boost::shared_ptr<path_generator_type> pathGenerator() const {
Size factors = this->process()->factors();
TimeGrid grid = timeGrid();
Size steps = grid.size() - 1;
typename RNG::rsg_type gen = RNG::make_sequence_generator(factors * steps, seed_);
return boost::make_shared<path_generator_type>(this->process(), grid, gen, false);
}
inline
ext::shared_ptr<typename MCDigitalEngine<RNG,S>::path_pricer_type>
MCDigitalEngine<RNG,S>::pathPricer() const {
ext::shared_ptr<CashOrNothingPayoff> payoff =
ext::dynamic_pointer_cast<CashOrNothingPayoff>(
this->arguments_.payoff);
QL_REQUIRE(payoff, "wrong payoff given");
ext::shared_ptr<AmericanExercise> exercise =
ext::dynamic_pointer_cast<AmericanExercise>(
this->arguments_.exercise);
QL_REQUIRE(exercise, "wrong exercise given");
ext::shared_ptr<GeneralizedBlackScholesProcess> process =
ext::dynamic_pointer_cast<GeneralizedBlackScholesProcess>(
this->process_);
QL_REQUIRE(process, "Black-Scholes process required");
TimeGrid grid = this->timeGrid();
PseudoRandom::ursg_type sequenceGen(grid.size()-1,
PseudoRandom::urng_type(76));
return ext::shared_ptr<
typename MCDigitalEngine<RNG,S>::path_pricer_type>(
new DigitalPathPricer(payoff,
exercise,
process->riskFreeRate(),
process,
sequenceGen));
}
boost::shared_ptr<Lattice>
BlackKarasinski::tree(const TimeGrid& grid) const {
TermStructureFittingParameter phi(termStructure());
boost::shared_ptr<ShortRateDynamics> numericDynamics(
new Dynamics(phi, a(), sigma()));
boost::shared_ptr<TrinomialTree> trinomial(
new TrinomialTree(numericDynamics->process(), grid));
boost::shared_ptr<ShortRateTree> numericTree(
new ShortRateTree(trinomial, numericDynamics, grid));
typedef TermStructureFittingParameter::NumericalImpl NumericalImpl;
boost::shared_ptr<NumericalImpl> impl =
boost::dynamic_pointer_cast<NumericalImpl>(phi.implementation());
impl->reset();
Real value = 1.0;
Real vMin = -50.0;
Real vMax = 50.0;
for (Size i=0; i<(grid.size() - 1); i++) {
Real discountBond = termStructure()->discount(grid[i+1]);
Real xMin = trinomial->underlying(i, 0);
Real dx = trinomial->dx(i);
Helper finder(i, xMin, dx, discountBond, numericTree);
Brent s1d;
s1d.setMaxEvaluations(1000);
value = s1d.solve(finder, 1e-7, value, vMin, vMax);
impl->set(grid[i], value);
// vMin = value - 10.0;
// vMax = value + 10.0;
}
return numericTree;
}
template <class PathType> inline
LongstaffSchwartzPathPricer<PathType>::LongstaffSchwartzPathPricer(
const TimeGrid& times,
const boost::shared_ptr<EarlyExercisePathPricer<PathType> >&
pathPricer,
const boost::shared_ptr<YieldTermStructure>& termStructure)
: calibrationPhase_(true),
pathPricer_(pathPricer),
coeff_ (new Array[times.size()-1]),
dF_ (new DiscountFactor[times.size()-1]),
v_ (pathPricer_->basisSystem()) {
for (Size i=0; i<times.size()-1; ++i) {
dF_[i] = termStructure->discount(times[i+1])
/ termStructure->discount(times[i]);
}
}
boost::shared_ptr<path_generator_type> pathGenerator() const {
TimeGrid grid = this->timeGrid();
typename RNG::rsg_type gen =
RNG::make_sequence_generator(grid.size()-1,seed_);
return boost::shared_ptr<path_generator_type>(
new path_generator_type(process_, grid,
gen, brownianBridge_));
}
boost::shared_ptr<path_generator_type> pathGenerator() const {
Size dimensions = process_->factors();
TimeGrid grid = this->timeGrid();
typename RNG::rsg_type generator =
RNG::make_sequence_generator(dimensions*(grid.size()-1),seed_);
return boost::shared_ptr<path_generator_type>(
new path_generator_type(process_, grid,
generator, brownianBridge_));
}
void HifivePricer::initializeImpl(const TimeGrid& timeGrid,
const boost::shared_ptr<YieldTermStructure>& discountCurve,
const boost::shared_ptr<PathGeneratorFactory>& pathGenFactory)
{
//this->discount_ = Array(eventTriggerList_.size(),1.0);
//for ( Size i = 0 ; i < eventTriggerList_.size() ; i++ )
//{
// eventTriggerList_[i]->initialize(timeGrid,discountCurve);
// if ( eventTriggerList_[i]->isExpired() )
// {
// remainEventPosition_ = i + 1;
// this->discount_[i] = 1.0;
// }else
// {
// this->discount_[i] = discountCurve_->discount(eventTriggerList_[i]->payoffDate());
// }
//}
Date today = Settings::instance().evaluationDate();
remainEventPosition_ = 0;
autoCallEventPosition_ = timeGrid.size() - 1;
this->cf_results_ = std::vector<boost::shared_ptr<CashFlowResult>>( this->eventTriggerList_.size() );
this->calcValue_results_ = std::vector<boost::shared_ptr<CalcValueResult>>(1);
this->calcValue_results_[0] = boost::shared_ptr<CalcValueResult>(
new CalcValueResult("NET","KRW"));
for ( Size i = 0 ; i < eventTriggerList_.size() ; i++ )
{
this->eventTriggerList_[i]->initialize(timeGrid,discountCurve,pathGenFactory);
this->cf_results_[i] = boost::shared_ptr<CashFlowResult>(
new CashFlowResult(i+1,
this->eventTriggerList_[i]->getEventDate(),
this->eventTriggerList_[i]->getPayoffDate(),
"NET",
this->currency_,
this->payoffDateInfo_->discount()) );
bool kk = eventTriggerList_[i]->isExpired();
if ( eventTriggerList_[i]->isExpired() )
{
remainEventPosition_ = i + 1;
}
}
this->kiBarrierEventTrigger_->initialize(timeGrid,discountCurve,pathGenFactory);
//this->nonOccBarrierEventTrigger_->initialize(timeGrid,discountCurve,pathGenFactory);
//pastkiBarrierEventOcc_ = kiBarrierEventTrigger_->pastEventOcc();
}
MultiPathGeneratorFixedPath<GSG>::MultiPathGeneratorFixedPath(
const boost::shared_ptr<StochasticProcess>& process,
const TimeGrid& times,
GSG generator,
bool brownianBridge)
: brownianBridge_(brownianBridge), process_(process),
generator_(generator), next_(boost::shared_ptr<MultiPath>(new MultiPath(process->size(), times)))
{
nextPtr_ = next_.get();
QL_REQUIRE(generator_.dimension() ==
process->factors()*(times.size()-1),
"dimension (" << generator_.dimension()
<< ") is not equal to ("
<< process->factors() << " * " << times.size()-1
<< ") the number of factors "
<< "times the number of time steps");
QL_REQUIRE(times.size() > 1,
"no times given");
}
ext::shared_ptr<path_generator_type> pathGenerator() const {
Size numAssets = processes_->size();
TimeGrid grid = timeGrid();
typename RNG::rsg_type gen =
RNG::make_sequence_generator(numAssets*(grid.size()-1),seed_);
return ext::shared_ptr<path_generator_type>(
new path_generator_type(processes_,
grid, gen, brownianBridge_));
}
inline
boost::shared_ptr<typename
MCLongstaffSchwartzEngine<GenericEngine,MC,RNG,S>::path_generator_type>
MCLongstaffSchwartzEngine<GenericEngine,MC,RNG,S>::pathGenerator() const {
Size dimensions = process_->factors();
TimeGrid grid = this->timeGrid();
typename RNG::rsg_type generator =
RNG::make_sequence_generator(dimensions*(grid.size()-1),seed_);
return boost::shared_ptr<path_generator_type>(
new path_generator_type(process_,
grid, generator, brownianBridge_));
}
MultiPathGenerator<GSG>::MultiPathGenerator(
const boost::shared_ptr<StochasticProcess>& process,
const TimeGrid& times,
GSG generator,
bool brownianBridge)
: brownianBridge_(brownianBridge), process_(process),
generator_(generator), next_(MultiPath(process->size(), times), 1.0) {
//std::cout << "dimension (" << generator_.dimension()
// << ") is not equal to ("
// << process->factors() << " * " << times.size() - 1
// << ") the number of factors "
// << "times the number of time steps";
QL_REQUIRE(generator_.dimension() ==
process->factors()*(times.size()-1),
"dimension (" << generator_.dimension()
<< ") is not equal to ("
<< process->factors() << " * " << times.size()-1
<< ") the number of factors "
<< "times the number of time steps");
QL_REQUIRE(times.size() > 1,
"no times given");
}
void simulateMP(const boost::shared_ptr<StochasticProcess>& process,
int nbPaths, TimeGrid& grid, BigNatural seed,
bool antithetic_variates, double *res) {
typedef PseudoRandom::rsg_type rsg_type;
typedef MultiPathGenerator<rsg_type>::sample_type sample_type;
Size assets = process->factors();
rsg_type rsg = PseudoRandom::make_sequence_generator(
(grid.size() - 1) * assets, seed);
MultiPathGenerator<rsg_type> generator(process, grid, rsg, false);
// fill simulated paths
for (int i=0; i<nbPaths; ++i) {
const bool antithetic = (i%2)==0 ? false : true;
sample_type sample = antithetic_variates ?
(antithetic ? generator.antithetic(): generator.next()) :
generator.next();
Path p1 = sample.value[0];
std::copy(p1.begin(), p1.end(), res + i * grid.size());
}
}
boost::shared_ptr<path_generator_type> pathGenerator() const {
boost::shared_ptr<BasketPayoff> payoff =
boost::dynamic_pointer_cast<BasketPayoff>(
arguments_.payoff);
QL_REQUIRE(payoff, "non-basket payoff given");
Size numAssets = processes_->size();
TimeGrid grid = timeGrid();
typename RNG::rsg_type gen =
RNG::make_sequence_generator(numAssets*(grid.size()-1),seed_);
return boost::shared_ptr<path_generator_type>(
new path_generator_type(processes_,
grid, gen, brownianBridge_));
}
inline
boost::shared_ptr<typename MCPathBasketEngine<RNG,S>::path_generator_type>
MCPathBasketEngine<RNG,S>::pathGenerator() const {
boost::shared_ptr<PathPayoff> payoff = arguments_.payoff;
QL_REQUIRE(payoff, "non-basket payoff given");
Size numAssets = process_->size();
TimeGrid grid = timeGrid();
typename RNG::rsg_type gen =
RNG::make_sequence_generator(numAssets * (grid.size() - 1), seed_);
return boost::shared_ptr<path_generator_type>(
new path_generator_type(process_,
grid, gen, brownianBridge_));
}
boost::shared_ptr<path_generator_type> pathGenerator() const {
Handle<YieldTermStructure> curve = model_->termStructure();
Date referenceDate = curve->referenceDate();
DayCounter dayCounter = curve->dayCounter();
Time forwardMeasureTime =
dayCounter.yearFraction(referenceDate,
arguments_.endDates.back());
Array parameters = model_->params();
Real a = parameters[0], sigma = parameters[1];
boost::shared_ptr<HullWhiteForwardProcess> process(
new HullWhiteForwardProcess(curve, a, sigma));
process->setForwardMeasureTime(forwardMeasureTime);
TimeGrid grid = this->timeGrid();
typename RNG::rsg_type generator =
RNG::make_sequence_generator(grid.size()-1,seed_);
return boost::shared_ptr<path_generator_type>(
new path_generator_type(process, grid, generator,
brownianBridge_));
}
boost::shared_ptr<path_generator_type> pathGenerator() const {
if(ifConst) {
Date exercisedate = GenericEngine<OneAssetOption::arguments,OneAssetOption::results>::arguments_.exercise->lastDate();
boost::shared_ptr<BlackScholesConstProcess> constProcess_(
new BlackScholesConstProcess(
exercisedate,
realProcess->stateVariable(),
realProcess->dividendYield(),
realProcess->riskFreeRate(),
realProcess->blackVolatility()
));
Size dimensions = constProcess_->factors();
TimeGrid grid = this->timeGrid();
typename RNG::rsg_type generator =
RNG::make_sequence_generator(dimensions*(grid.size()-1),seed_);
return boost::shared_ptr<path_generator_type>(
new path_generator_type(constProcess_, grid,
generator, brownianBridge_));
} else {
return MCEuropeanEngine<RNG,S>::pathGenerator();
}
};
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);
}
}
LongstaffSchwartzProxyPathPricer::LongstaffSchwartzProxyPathPricer(
const TimeGrid ×,
const boost::shared_ptr<EarlyExercisePathPricer<PathType> > &pricer,
const boost::shared_ptr<YieldTermStructure> &termStructure)
: LongstaffSchwartzPathPricer<PathType>(times, pricer, termStructure),
coeffItm_(times.size() - 1), coeffOtm_(times.size() - 1) {}