inline void MultiPathGeneratorFixedPath<GSG>::next() const
{
typedef typename GSG::sample_type sequence_type;
const sequence_type& sequence_ = generator_.nextSequence();
Size m = process_->size();
Size n = process_->factors();
MultiPath& path = *nextPtr_;
Array asset = process_->initialValues();
for (Size j=0; j<m; j++)
path[j].front() = asset[j];
Array temp(n);
TimeGrid timeGrid = path[0].timeGrid();
Time t, dt;
for (Size i = 1; i < path.pathSize(); i++) {
Size offset = (i-1)*n;
t = timeGrid[i-1];
dt = timeGrid.dt(i-1);
std::copy(sequence_.value.begin()+offset,
sequence_.value.begin()+offset+n,
temp.begin());
asset = process_->evolve(t, asset, dt, temp,i-1);
for (Size j=0; j<m; j++)
path[j][i] = asset[j];
}
}
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);
}
}
}
Real DigitalPathPricer::operator()(const Path& path) const {
Size n = path.length();
QL_REQUIRE(n>1, "the path cannot be empty");
Real log_asset_price = std::log(path.front());
Real x, y;
Volatility vol;
TimeGrid timeGrid = path.timeGrid();
Time dt;
std::vector<Real> u = sequenceGen_.nextSequence().value;
Real log_strike = std::log(payoff_->strike());
Size i;
switch (payoff_->optionType()) {
case Option::Call:
for (i=0; i<n-1; i++) {
x = std::log(path[i+1]/path[i]);
// terminal or initial vol?
vol = diffProcess_->diffusion(timeGrid[i+1],
std::exp(log_asset_price));
// vol = diffProcess_->diffusion(timeGrid[i+2],
// std::exp(log_asset_price+x));
dt = timeGrid.dt(i);
y = log_asset_price +
0.5*(x + std::sqrt(x*x-2*vol*vol*dt*std::log((1-u[i]))));
// cross the strike
if (y >= log_strike) {
if (exercise_->payoffAtExpiry()) {
return payoff_->cashPayoff() *
discountTS_->discount(path.timeGrid().back());
} else {
// the discount should be calculated at the exercise
// time between path.timeGrid()[i+1] and
// path.timeGrid()[i+2]
return payoff_->cashPayoff() *
discountTS_->discount(path.timeGrid()[i+1]);
}
}
log_asset_price += x;
}
break;
case Option::Put:
for (i=0; i<n-1; i++) {
x = std::log(path[i+1]/path[i]);
// terminal or initial vol?
// initial (timeGrid[i+1]) for the time being
vol = diffProcess_->diffusion(timeGrid[i+1],
std::exp(log_asset_price));
// vol = diffProcess_->diffusion(timeGrid[i+2],
// std::exp(log_asset_price+x));
dt = timeGrid.dt(i);
y = log_asset_price +
0.5*(x - std::sqrt(x*x - 2*vol*vol*dt*std::log(u[i])));
if (y <= log_strike) {
if (exercise_->payoffAtExpiry()) {
return payoff_->cashPayoff() *
discountTS_->discount(path.timeGrid().back());
} else {
// the discount should be calculated at the exercise
// time between path.timeGrid()[i+1] and
// path.timeGrid()[i+2]
return payoff_->cashPayoff() *
discountTS_->discount(path.timeGrid()[i+1]);
}
}
log_asset_price += x;
}
break;
default:
QL_FAIL("unknown option type");
}
return 0.0;
}