//! discount factor implied by the rate compounded between two dates
DiscountFactor discountFactor(const Date& d1,
const Date& d2,
const Date& refStart = Date(),
const Date& refEnd = Date()) const {
QL_REQUIRE(d2>=d1,
"d1 (" << d1 << ") "
"later than d2 (" << d2 << ")");
Time t = dc_.yearFraction(d1, d2, refStart, refEnd);
return discountFactor(t);
}
Real LiborCurve::swapAnnuity(Size reference, Size fixing, Size length, Size payFreq) {
QL_REQUIRE(reference<=fixing,"reference index " << reference << " must be leq fixing " << fixing);
Size pf = payFreq;
double sum=0.0;
double p=1.0;
for(int j=fixing;j<fixing+length;j++) {
p*=1.0/(1.0+(rateTimes_[j+1]-rateTimes_[j])*rates_[j]);
if(--pf == 0) { sum+=p*(rateTimes_[j+1]-rateTimes_[j+1-payFreq]); pf=payFreq; }
}
//printf("swap Annuity=%1.11f\n",discountFactor(reference,fixing)*sum);
return discountFactor(reference,fixing)*sum;
}
void FFTEngine::precalculate(const std::vector<boost::shared_ptr<Instrument> >& optionList) {
// Group payoffs by expiry date
// as with FFT we can compute a bunch of these at once
resultMap_.clear();
typedef std::vector<boost::shared_ptr<StrikedTypePayoff> > PayoffList;
typedef std::map<Date, PayoffList> PayoffMap;
PayoffMap payoffMap;
for (std::vector<boost::shared_ptr<Instrument> >::const_iterator optIt = optionList.begin();
optIt != optionList.end(); optIt++)
{
boost::shared_ptr<VanillaOption> option = boost::dynamic_pointer_cast<VanillaOption>(*optIt);
QL_REQUIRE(option, "instrument must be option");
QL_REQUIRE(option->exercise()->type() == Exercise::European,
"not an European Option");
boost::shared_ptr<StrikedTypePayoff> payoff =
boost::dynamic_pointer_cast<StrikedTypePayoff>(option->payoff());
QL_REQUIRE(payoff, "non-striked payoff given");
payoffMap[option->exercise()->lastDate()].push_back(payoff);
}
std::complex<Real> i1(0, 1);
Real alpha = 1.25;
for (PayoffMap::const_iterator payIt = payoffMap.begin(); payIt != payoffMap.end(); payIt++)
{
Date expiryDate = payIt->first;
// Calculate n large enough for maximum strike, and round up to a power of 2
Real maxStrike = 0.0;
for (PayoffList::const_iterator it = payIt->second.begin();
it != payIt->second.end(); it++)
{
boost::shared_ptr<StrikedTypePayoff> payoff = *it;
if (payoff->strike() > maxStrike)
maxStrike = payoff->strike();
}
Real nR = 2.0 * (std::log(maxStrike) + lambda_) / lambda_;
Size log2_n = (static_cast<Size>((std::log(nR) / std::log(2.0))) + 1);
Size n = 1 << log2_n;
// Strike range (equation 19,20)
Real b = n * lambda_ / 2.0;
// Grid spacing (equation 23)
Real eta = 2.0 * M_PI / (lambda_ * n);
// Discount factor
Real df = discountFactor(expiryDate);
Real div = dividendYield(expiryDate);
// Input to fourier transform
std::vector<std::complex<Real> > fti;
fti.resize(n);
// Precalculate any discount factors etc.
precalculateExpiry(expiryDate);
for (Size i=0; i<n; i++)
{
Real k_u = -b + lambda_ * i;
Real v_j = eta * i;
Real sw = eta * (3.0 + ((i % 2) == 0 ? -1.0 : 1.0) - ((i == 0) ? 1.0 : 0.0)) / 3.0;
std::complex<Real> psi = df * complexFourierTransform(v_j - (alpha + 1)* i1);
psi = psi / (alpha*alpha + alpha - v_j*v_j + i1 * (2 * alpha + 1.0) * v_j);
fti[i] = std::exp(i1 * b * v_j) * sw * psi;
}
// Perform fft
std::vector<std::complex<Real> > results(n);
FastFourierTransform fft(log2_n);
fft.transform(fti.begin(), fti.end(), results.begin());
// Call prices
std::vector<Real> prices, strikes;
prices.resize(n);
strikes.resize(n);
for (Size i=0; i<n; i++)
{
Real k_u = -b + lambda_ * i;
prices[i] = (std::exp(-alpha * k_u) / M_PI) * results[i].real();
strikes[i] = std::exp(k_u);
}
for (PayoffList::const_iterator it = payIt->second.begin();
it != payIt->second.end(); it++)
{
boost::shared_ptr<StrikedTypePayoff> payoff = *it;
Real callPrice = LinearInterpolation(strikes.begin(), strikes.end(), prices.begin())(payoff->strike());
switch (payoff->optionType())
{
case Option::Call:
resultMap_[expiryDate][payoff] = callPrice;
break;
case Option::Put:
resultMap_[expiryDate][payoff] = callPrice - process_->x0() * div + payoff->strike() * df;
break;
default:
QL_FAIL("Invalid option type");
}
}
}
}
Real LiborCurve::swap2TerminalMeasure(Size reference, Size fixing, Size delay, Size length, Size payFreq) {
return discountFactor(reference,fixing+delay)/discountFactorT0(0,fixing+delay) *
swapAnnuityT0(fixing,length,payFreq)/swapAnnuity(reference,fixing,length,payFreq);
}
Real LiborCurve::rRate(Size reference, Size fixing, Size delay, Size length, Size payFreq) {
QL_REQUIRE(reference<=fixing,"reference index " << reference << " must be leq fixing " << fixing);
double sumD=rateTimes_[fixing+length]-rateTimes_[fixing];
return swapAnnuityT0(fixing,length,payFreq)/(discountFactorT0(0,fixing+delay)*sumD)*
(discountFactor(reference,fixing+delay)*sumD/swapAnnuity(reference,fixing,length,payFreq)-1.0);
}
double CCRate::forwardRate(double t1, double t2) {
double f = 1.0 / (t2 - t1) *
(discountFactor(t1)
/ discountFactor(t2) - 1);
return f;
}
