Volatility BlackVolTermStructure::blackForwardVol(Time time1,
Time time2,
Real strike,
bool extrapolate) const {
QL_REQUIRE(time1 <= time2,
time1 << " later than " << time2);
checkRange(time2, extrapolate);
checkStrike(strike, extrapolate);
if (time2==time1) {
if (time1==0.0) {
Time epsilon = 1.0e-5;
Real var = blackVarianceImpl(epsilon, strike);
return std::sqrt(var/epsilon);
} else {
Time epsilon = std::min<Time>(1.0e-5, time1);
Real var1 = blackVarianceImpl(time1-epsilon, strike);
Real var2 = blackVarianceImpl(time1+epsilon, strike);
QL_ENSURE(var2>=var1,
"variances must be non-decreasing");
return std::sqrt((var2-var1)/(2*epsilon));
}
} else {
Real var1 = blackVarianceImpl(time1, strike);
Real var2 = blackVarianceImpl(time2, strike);
QL_ENSURE(var2 >= var1,
"variances must be non-decreasing");
return std::sqrt((var2-var1)/(time2-time1));
}
}
Real BlackVolTermStructure::blackForwardVariance(Time time1,
Time time2,
Real strike,
bool extrapolate) const {
QL_REQUIRE(time1 <= time2,
time1 << " later than " << time2);
checkRange(time2, extrapolate);
checkStrike(strike, extrapolate);
Real v1 = blackVarianceImpl(time1, strike);
Real v2 = blackVarianceImpl(time2, strike);
QL_ENSURE(v2 >= v1,
"variances must be non-decreasing");
return v2-v1;
}
inline Real BlackVolTermStructure::blackVariance(Time t,
Real strike,
bool extrapolate) const {
checkRange(t, extrapolate);
checkStrike(strike, extrapolate);
return blackVarianceImpl(t, strike);
}
inline
Volatility BlackVarianceTermStructure ::blackVolImpl(Time t,
Real strike) const {
Time nonZeroMaturity = (t==0.0 ? 0.00001 : t);
Real var = blackVarianceImpl(nonZeroMaturity, strike);
return std::sqrt(var/nonZeroMaturity);
}
inline Real BlackVolTermStructure::blackVariance(const Date& d,
Real strike,
bool extrapolate) const {
checkRange(d, extrapolate);
checkStrike(strike, extrapolate);
Time t = timeFromReference(d);
return blackVarianceImpl(t, strike);
}