Real GeneralizedBlackScholesProcess::stdDeviation(Time t0, Real x0, Time dt) const {
localVolatility(); // trigger update
if(isStrikeIndependent_ && !forceDiscretization_) {
// exact value for curves
return std::sqrt(variance(t0,x0,dt));
}
else{
return discretization_->diffusion(*this,t0,x0,dt);
}
}
Real GeneralizedBlackScholesProcess::variance(Time t0, Real x0, Time dt) const {
localVolatility(); // trigger update
if(isStrikeIndependent_ && !forceDiscretization_) {
// exact value for curves
return blackVolatility_->blackVariance(t0 + dt, 0.01) -
blackVolatility_->blackVariance(t0, 0.01);
}
else{
return discretization_->variance(*this,t0,x0,dt);
}
}
Real GeneralizedBlackScholesProcess::expectation(Time t0,
Real x0,
Time dt) const {
localVolatility(); // trigger update
if(isStrikeIndependent_ && !forceDiscretization_) {
// exact value for curves
return x0 *
std::exp(dt * (riskFreeRate_->forwardRate(t0, t0 + dt, Continuous,
NoFrequency, true) -
dividendYield_->forwardRate(
t0, t0 + dt, Continuous, NoFrequency, true)));
} else {
QL_FAIL("not implemented");
}
}
Real GeneralizedBlackScholesProcess::evolve(Time t0, Real x0,
Time dt, Real dw) const {
localVolatility(); // trigger update
if (isStrikeIndependent_ && !forceDiscretization_) {
// exact value for curves
Real var = variance(t0, x0, dt);
Real drift = (riskFreeRate_->forwardRate(t0, t0 + dt, Continuous,
NoFrequency, true) -
dividendYield_->forwardRate(t0, t0 + dt, Continuous,
NoFrequency, true)) *
dt -
0.5 * var;
return apply(x0, std::sqrt(var) * dw + drift);
} else
return apply(x0, discretization_->drift(*this, t0, x0, dt) +
stdDeviation(t0, x0, dt) * dw);
}
Real VarianceGammaProcess::diffusion(Time t, Real x) const
{
return localVolatility()->localVol(t, x, true);
}
Real GeneralizedBlackScholesProcess::diffusion(Time t, Real x) const {
return localVolatility()->localVol(t, x, true);
}
