template <class PathType> inline
void LongstaffSchwartzPathPricer<PathType>::calibrate() {
const Size n = paths_.size();
Array prices(n), exercise(n);
const Size len = EarlyExerciseTraits<PathType>::pathLength(paths_[0]);
for (Size i=0; i<n; ++i)
prices[i] = (*pathPricer_)(paths_[i], len-1);
std::vector<Real> y;
std::vector<StateType> x;
for (Size i=len-2; i>0; --i) {
y.clear();
x.clear();
//roll back step
for (Size j=0; j<n; ++j) {
exercise[j]=(*pathPricer_)(paths_[j], i);
if (exercise[j]>0.0) {
x.push_back(pathPricer_->state(paths_[j], i));
y.push_back(dF_[i]*prices[j]);
}
}
if (v_.size() <= x.size()) {
coeff_[i] = GeneralLinearLeastSquares(x, y, v_).coefficients();
}
else {
// if number of itm paths is smaller then the number of
// calibration functions then early exercise if exerciseValue > 0
coeff_[i] = Array(v_.size(), 0.0);
}
for (Size j=0, k=0; j<n; ++j) {
prices[j]*=dF_[i];
if (exercise[j]>0.0) {
Real continuationValue = 0.0;
for (Size l=0; l<v_.size(); ++l) {
continuationValue += coeff_[i][l] * v_[l](x[k]);
}
if (continuationValue < exercise[j]) {
prices[j] = exercise[j];
}
++k;
}
}
}
// remove calibration paths and release memory
std::vector<PathType> empty;
paths_.swap(empty);
// entering the calculation phase
calibrationPhase_ = false;
}
void LongstaffSchwartzProxyPathPricer::post_processing(
const Size i, const std::vector<StateType> &state,
const std::vector<Real> &price, const std::vector<Real> &exercise) {
std::vector<StateType> x_itm, x_otm;
std::vector<Real> y_itm, y_otm;
cutoff_ = -QL_MAX_REAL;
for (Size j = 0; j < state.size(); ++j) {
if (exercise[j] > 0.0) {
x_itm.push_back(state[j]);
y_itm.push_back(price[j]);
} else {
x_otm.push_back(state[j]);
y_otm.push_back(price[j]);
if(state[j]>cutoff_)
cutoff_ = state[j];
}
}
if (v_.size() <= x_itm.size()) {
coeffItm_[i - 1] =
GeneralLinearLeastSquares(x_itm, y_itm, v_).coefficients();
} else {
// see longstaffschwartzpricer.hpp
coeffItm_[i - 1] = Array(v_.size(), 0.0);
}
if (v_.size() <= x_otm.size()) {
coeffOtm_[i - 1] =
GeneralLinearLeastSquares(x_otm, y_otm, v_).coefficients();
} else {
// see longstaffschwartzpricer.hpp
coeffOtm_[i - 1] = Array(v_.size(), 0.0);
}
}
template <class PathType> inline
void LongstaffSchwartzPathPricer<PathType>::calibrate() {
#ifdef _OPENMP
for (Size i = 0; i < pathsMt_.size(); ++i) {
paths_.insert(paths_.end(), pathsMt_[i].begin(), pathsMt_[i].end());
}
#endif
const Size n = paths_.size();
Array prices(n), exercise(n);
std::vector<StateType> p_state(n);
std::vector<Real> p_price(n), p_exercise(n);
for (Size i=0; i<n; ++i) {
p_state[i] = pathPricer_->state(paths_[i],len_-1);
prices[i] = p_price[i] = (*pathPricer_)(paths_[i], len_-1);
p_exercise[i] = prices[i];
}
post_processing(len_ - 1, p_state, p_price, p_exercise);
std::vector<Real> y;
std::vector<StateType> x;
for (Size i=len_-2; i>0; --i) {
y.clear();
x.clear();
//roll back step
for (Size j=0; j<n; ++j) {
exercise[j]=(*pathPricer_)(paths_[j], i);
if (exercise[j]>0.0) {
x.push_back(pathPricer_->state(paths_[j], i));
y.push_back(dF_[i]*prices[j]);
}
}
if (v_.size() <= x.size()) {
coeff_[i-1] = GeneralLinearLeastSquares(x, y, v_).coefficients();
}
else {
// if number of itm paths is smaller then the number of
// calibration functions then early exercise if exerciseValue > 0
coeff_[i-1] = Array(v_.size(), 0.0);
}
for (Size j=0, k=0; j<n; ++j) {
prices[j]*=dF_[i];
if (exercise[j]>0.0) {
Real continuationValue = 0.0;
for (Size l=0; l<v_.size(); ++l) {
continuationValue += coeff_[i-1][l] * v_[l](x[k]);
}
if (continuationValue < exercise[j]) {
prices[j] = exercise[j];
}
++k;
}
p_state[j] = pathPricer_->state(paths_[j],i);
p_price[j] = prices[j];
p_exercise[j] = exercise[j];
}
post_processing(i, p_state, p_price, p_exercise);
}
// remove calibration paths and release memory
std::vector<PathType> empty;
paths_.swap(empty);
// entering the calculation phase
calibrationPhase_ = false;
}
void LongstaffSchwartzMultiPathPricer::calibrate() {
const Size n = paths_.size(); // number of paths
Array prices(n, 0.0), exercise(n, 0.0);
const Size basisDimension = payoff_->basisSystemDimension();
const Size len = paths_[0].pathLength();
/*
We try to estimate the lower bound of the continuation value,
so that only itm paths contribute to the regression.
*/
for (Size j = 0; j < n; ++j) {
const Real payoff = paths_[j].payments[len - 1];
const Real exercise = paths_[j].exercises[len - 1];
const Array & states = paths_[j].states[len - 1];
const bool canExercise = !states.empty();
// at the end the continuation value is 0.0
if (canExercise && exercise > 0.0)
prices[j] += exercise;
prices[j] += payoff;
}
lowerBounds_[len - 1] = *std::min_element(prices.begin(), prices.end());
std::vector<bool> lsExercise(n);
for (Integer i = len - 2; i >= 0; --i) {
std::vector<Real> y;
std::vector<Array> x;
// prices are discounted up to time i
const Real discountRatio = dF_[i + 1] / dF_[i];
prices *= discountRatio;
lowerBounds_[i + 1] *= discountRatio;
//roll back step
for (Size j = 0; j < n; ++j) {
exercise[j] = paths_[j].exercises[i];
// If states is empty, no exercise in this path
// and the path will not partecipate to the Lesat Square regression
const Array & states = paths_[j].states[i];
QL_REQUIRE(states.empty() || states.size() == basisDimension,
"Invalid size of basis system");
// only paths that could potentially create exercise opportunities
// partecipate to the regression
// if exercise is lower than minimum continuation value, no point in considering it
if (!states.empty() && exercise[j] > lowerBounds_[i + 1]) {
x.push_back(states);
y.push_back(prices[j]);
}
}
if (v_.size() <= x.size()) {
coeff_[i] = GeneralLinearLeastSquares(x, y, v_).coefficients();
}
else {
// if number of itm paths is smaller then the number of
// calibration functions -> never exercise
QL_TRACE("Not enough itm paths: default decision is NEVER");
coeff_[i] = Array(0);
}
/* attempt to avoid static arbitrage given by always or never exercising.
always is absolute: regardless of the lowerBoundContinuationValue_ (this could be changed)
but it still honours "canExercise"
*/
Real sumOptimized = 0.0;
Real sumNoExercise = 0.0;
Real sumAlwaysExercise = 0.0; // always, if allowed
for (Size j = 0, k = 0; j < n; ++j) {
sumNoExercise += prices[j];
lsExercise[j] = false;
const bool canExercise = !paths_[j].states[i].empty();
if (canExercise) {
sumAlwaysExercise += exercise[j];
if (!coeff_[i].empty() && exercise[j] > lowerBounds_[i + 1]) {
Real continuationValue = 0.0;
for (Size l = 0; l < v_.size(); ++l) {
continuationValue += coeff_[i][l] * v_[l](x[k]);
}
if (continuationValue < exercise[j]) {
lsExercise[j] = true;
}
++k;
}
}
else {
sumAlwaysExercise += prices[j];
}
sumOptimized += lsExercise[j] ? exercise[j] : prices[j];
}
sumOptimized /= n;
sumNoExercise /= n;
sumAlwaysExercise /= n;
QL_TRACE( "Time index: " << i
<< ", LowerBound: " << lowerBounds_[i + 1]
<< ", Optimum: " << sumOptimized
<< ", Continuation: " << sumNoExercise
<< ", Termination: " << sumAlwaysExercise);
if ( sumOptimized >= sumNoExercise
&& sumOptimized >= sumAlwaysExercise) {
QL_TRACE("Accepted LS decision");
for (Size j = 0; j < n; ++j) {
// lsExercise already contains "canExercise"
prices[j] = lsExercise[j] ? exercise[j] : prices[j];
}
}
else if (sumAlwaysExercise > sumNoExercise) {
QL_TRACE("Overridden bad LS decision: ALWAYS");
for (Size j = 0; j < n; ++j) {
const bool canExercise = !paths_[j].states[i].empty();
prices[j] = canExercise ? exercise[j] : prices[j];
}
// special value to indicate always exercise
coeff_[i] = Array(v_.size() + 1);
}
else {
QL_TRACE("Overridden bad LS decision: NEVER");
// prices already contain the continuation value
// special value to indicate never exercise
coeff_[i] = Array(0);
}
// then we add in any case the payment at time t
// which is made even if cancellation happens at t
for (Size j = 0; j < n; ++j) {
const Real payoff = paths_[j].payments[i];
prices[j] += payoff;
}
lowerBounds_[i] = *std::min_element(prices.begin(), prices.end());
}
// remove calibration paths
paths_.clear();
// entering the calculation phase
calibrationPhase_ = false;
}