// calculating swaption volatility matrix using
// Rebonatos approx. formula. Be aware that this
// matrix is valid only for regular fixings and
// assumes that the fix and floating leg have the
// same frequency
ext::shared_ptr<SwaptionVolatilityMatrix>
LiborForwardModel::getSwaptionVolatilityMatrix() const {
if (swaptionVola) {
return swaptionVola;
}
const ext::shared_ptr<IborIndex> index = process_->index();
const Date today = process_->fixingDates()[0];
const Size size=process_->size()/2;
Matrix volatilities(size, size);
std::vector<Date> exercises(process_->fixingDates().begin() + 1,
process_->fixingDates().begin() + size+1);
std::vector<Period> lengths(size);
for (Size i=0; i < size; ++i) {
lengths[i] = (i+1)*index->tenor();
}
const Array f = process_->initialValues();
for (Size k=0; k < size; ++k) {
const Size alpha =k;
const Time t_alpha=process_->fixingTimes()[alpha+1];
Matrix var(size, size);
for (Size i=alpha+1; i <= k+size; ++i) {
for (Size j=i; j <= k+size; ++j) {
var[i-alpha-1][j-alpha-1] = var[j-alpha-1][i-alpha-1] =
covarProxy_->integratedCovariance(i, j, t_alpha);
}
}
for (Size l=1; l <= size; ++l) {
const Size beta =l + k;
const Array w = w_0(alpha, beta);
Real sum=0.0;
for (Size i=alpha+1; i <= beta; ++i) {
for (Size j=alpha+1; j <= beta; ++j) {
sum+=w[i]*w[j]*f[i]*f[j]*var[i-alpha-1][j-alpha-1];
}
}
volatilities[k][l-1] =
std::sqrt(sum/t_alpha)/S_0(alpha, beta);
}
}
return swaptionVola = ext::make_shared<SwaptionVolatilityMatrix>(
today, exercises, lengths,
volatilities,
index->dayCounter());
}
SwaptionVolCube1::Cube
SwaptionVolCube1::sabrCalibration(const Cube& marketVolCube) const {
const std::vector<Time>& optionTimes = marketVolCube.optionTimes();
const std::vector<Time>& swapLengths = marketVolCube.swapLengths();
const std::vector<Date>& optionDates = marketVolCube.optionDates();
const std::vector<Period>& swapTenors = marketVolCube.swapTenors();
Matrix alphas(optionTimes.size(), swapLengths.size(),0.);
Matrix betas(alphas);
Matrix nus(alphas);
Matrix rhos(alphas);
Matrix forwards(alphas);
Matrix errors(alphas);
Matrix maxErrors(alphas);
Matrix endCriteria(alphas);
const std::vector<Matrix>& tmpMarketVolCube = marketVolCube.points();
std::vector<Real> strikes(strikeSpreads_.size());
std::vector<Real> volatilities(strikeSpreads_.size());
for (Size j=0; j<optionTimes.size(); j++) {
for (Size k=0; k<swapLengths.size(); k++) {
Rate atmForward = atmStrike(optionDates[j], swapTenors[k]);
strikes.clear();
volatilities.clear();
for (Size i=0; i<nStrikes_; i++){
Real strike = atmForward+strikeSpreads_[i];
if(strike>=MINSTRIKE) {
strikes.push_back(strike);
volatilities.push_back(tmpMarketVolCube[i][j][k]);
}
}
const std::vector<Real>& guess = parametersGuess_.operator()(
optionTimes[j], swapLengths[k]);
const boost::shared_ptr<SABRInterpolation> sabrInterpolation =
boost::shared_ptr<SABRInterpolation>(new
SABRInterpolation(strikes.begin(), strikes.end(),
volatilities.begin(),
optionTimes[j], atmForward,
guess[0], guess[1],
guess[2], guess[3],
isParameterFixed_[0],
isParameterFixed_[1],
isParameterFixed_[2],
isParameterFixed_[3],
vegaWeightedSmileFit_,
endCriteria_,
optMethod_,
errorAccept_,
useMaxError_,
maxGuesses_));
sabrInterpolation->update();
Real rmsError = sabrInterpolation->rmsError();
Real maxError = sabrInterpolation->maxError();
alphas [j][k] = sabrInterpolation->alpha();
betas [j][k] = sabrInterpolation->beta();
nus [j][k] = sabrInterpolation->nu();
rhos [j][k] = sabrInterpolation->rho();
forwards [j][k] = atmForward;
errors [j][k] = rmsError;
maxErrors [j][k] = maxError;
endCriteria[j][k] = sabrInterpolation->endCriteria();
QL_ENSURE(endCriteria[j][k]!=EndCriteria::MaxIterations,
"global swaptions calibration failed: "
"MaxIterations reached: " << "\n" <<
"option maturity = " << optionDates[j] << ", \n" <<
"swap tenor = " << swapTenors[k] << ", \n" <<
"error = " << io::rate(errors[j][k]) << ", \n" <<
"max error = " << io::rate(maxErrors[j][k]) << ", \n" <<
" alpha = " << alphas[j][k] << "n" <<
" beta = " << betas[j][k] << "\n" <<
" nu = " << nus[j][k] << "\n" <<
" rho = " << rhos[j][k] << "\n"
);
QL_ENSURE(useMaxError_ ? maxError : rmsError < maxErrorTolerance_,
"global swaptions calibration failed: "
"option tenor " << optionDates[j] <<
", swap tenor " << swapTenors[k] <<
(useMaxError_ ? ": max error " : ": error") <<
(useMaxError_ ? maxError : rmsError) <<
" alpha = " << alphas[j][k] << "n" <<
" beta = " << betas[j][k] << "\n" <<
" nu = " << nus[j][k] << "\n" <<
" rho = " << rhos[j][k] << "\n" <<
(useMaxError_ ? ": error" : ": max error ") <<
(useMaxError_ ? rmsError :maxError)
);
}
}
Cube sabrParametersCube(optionDates, swapTenors,
optionTimes, swapLengths, 8);
sabrParametersCube.setLayer(0, alphas);
sabrParametersCube.setLayer(1, betas);
sabrParametersCube.setLayer(2, nus);
sabrParametersCube.setLayer(3, rhos);
sabrParametersCube.setLayer(4, forwards);
sabrParametersCube.setLayer(5, errors);
sabrParametersCube.setLayer(6, maxErrors);
sabrParametersCube.setLayer(7, endCriteria);
return sabrParametersCube;
}
void SwaptionVolCube1::sabrCalibrationSection(
const Cube& marketVolCube,
Cube& parametersCube,
const Period& swapTenor) const {
const std::vector<Time>& optionTimes = marketVolCube.optionTimes();
const std::vector<Time>& swapLengths = marketVolCube.swapLengths();
const std::vector<Date>& optionDates = marketVolCube.optionDates();
const std::vector<Period>& swapTenors = marketVolCube.swapTenors();
Size k = std::find(swapTenors.begin(), swapTenors.end(),
swapTenor) - swapTenors.begin();
QL_REQUIRE(k != swapTenors.size(), "swap tenor not found");
std::vector<Real> calibrationResult(8,0.);
const std::vector<Matrix>& tmpMarketVolCube = marketVolCube.points();
std::vector<Real> strikes(strikeSpreads_.size());
std::vector<Real> volatilities(strikeSpreads_.size());
for (Size j=0; j<optionTimes.size(); j++) {
Rate atmForward = atmStrike(optionDates[j], swapTenors[k]);
strikes.clear();
volatilities.clear();
for (Size i=0; i<nStrikes_; i++){
Real strike = atmForward+strikeSpreads_[i];
if(strike>=MINSTRIKE) {
strikes.push_back(strike);
volatilities.push_back(tmpMarketVolCube[i][j][k]);
}
}
const std::vector<Real>& guess = parametersGuess_.operator()(
optionTimes[j], swapLengths[k]);
const boost::shared_ptr<SABRInterpolation> sabrInterpolation =
boost::shared_ptr<SABRInterpolation>(new
SABRInterpolation(strikes.begin(), strikes.end(),
volatilities.begin(),
optionTimes[j], atmForward,
guess[0], guess[1],
guess[2], guess[3],
isParameterFixed_[0],
isParameterFixed_[1],
isParameterFixed_[2],
isParameterFixed_[3],
vegaWeightedSmileFit_,
endCriteria_,
optMethod_,
errorAccept_,
useMaxError_,
maxGuesses_));
sabrInterpolation->update();
Real interpolationError = sabrInterpolation->rmsError();
calibrationResult[0]=sabrInterpolation->alpha();
calibrationResult[1]=sabrInterpolation->beta();
calibrationResult[2]=sabrInterpolation->nu();
calibrationResult[3]=sabrInterpolation->rho();
calibrationResult[4]=atmForward;
calibrationResult[5]=interpolationError;
calibrationResult[6]=sabrInterpolation->maxError();
calibrationResult[7]=sabrInterpolation->endCriteria();
QL_ENSURE(calibrationResult[7]!=EndCriteria::MaxIterations,
"section calibration failed: "
"option tenor " << optionDates[j] <<
", swap tenor " << swapTenors[k] <<
": max iteration (" <<
endCriteria_->maxIterations() << ")" <<
", alpha " << calibrationResult[0]<<
", beta " << calibrationResult[1] <<
", nu " << calibrationResult[2] <<
", rho " << calibrationResult[3] <<
", max error " << calibrationResult[6] <<
", error " << calibrationResult[5]
);
QL_ENSURE(useMaxError_ ? calibrationResult[6] : calibrationResult[5] < maxErrorTolerance_,
"section calibration failed: "
"option tenor " << optionDates[j] <<
", swap tenor " << swapTenors[k] <<
(useMaxError_ ? ": max error " : ": error ") <<
(useMaxError_ ? calibrationResult[6] : calibrationResult[5]) <<
", alpha " << calibrationResult[0] <<
", beta " << calibrationResult[1] <<
", nu " << calibrationResult[2] <<
", rho " << calibrationResult[3] <<
(useMaxError_ ? ": error" : ": max error ") <<
(useMaxError_ ? calibrationResult[5] : calibrationResult[6])
);
parametersCube.setPoint(optionDates[j], swapTenors[k],
optionTimes[j], swapLengths[k],
calibrationResult);
parametersCube.updateInterpolators();
}
}
Volatility PiecewiseConstantVariance::volatility(Size i) const {
QL_REQUIRE(i<volatilities().size(),
"invalid step index");
return volatilities()[i];
}
