Real unsafeShiftedSabrVolatility(Rate strike,
Rate forward,
Time expiryTime,
Real alpha,
Real beta,
Real nu,
Real rho,
Real shift) {
return unsafeSabrVolatility(strike+shift,forward+shift,expiryTime,
alpha,beta,nu,rho);
}
Real sabrVolatility(Rate strike,
Rate forward,
Time expiryTime,
Real alpha,
Real beta,
Real nu,
Real rho) {
QL_REQUIRE(strike>0.0, "strike must be positive: "
<< io::rate(strike) << " not allowed");
QL_REQUIRE(forward>0.0, "at the money forward rate must be "
"positive: " << io::rate(forward) << " not allowed");
QL_REQUIRE(expiryTime>=0.0, "expiry time must be non-negative: "
<< expiryTime << " not allowed");
validateSabrParameters(alpha, beta, nu, rho);
return unsafeSabrVolatility(strike, forward, expiryTime,
alpha, beta, nu, rho);
}
Real NoArbSabrSmileSection::volatilityImpl(Rate strike) const {
Real impliedVol = 0.0;
try {
Option::Type type;
if (strike >= forward_)
type = Option::Call;
else
type = Option::Put;
impliedVol =
blackFormulaImpliedStdDev(type, strike, forward_,
optionPrice(strike, type, 1.0), 1.0) /
std::sqrt(exerciseTime());
} catch (...) {
}
if (impliedVol == 0.0)
// fall back on Hagan 2002 expansion
impliedVol =
unsafeSabrVolatility(strike, forward_, exerciseTime(), params_[0],
params_[1], params_[2], params_[3]);
return impliedVol;
}
Real SabrSmileSection::volatilityImpl(Rate strike) const {
strike = std::max(0.00001,strike);
return unsafeSabrVolatility(strike, forward_,
exerciseTime(), alpha_, beta_, nu_, rho_);
}