How to efficiently shift BlackVarianceSurface to compute the vega, volga and vanna of an option

Question

I am working with a vol surface that was created as a BlackVarianceSurface. Now I would like to compute the "vol" greeks for a product and as such I need to shift that surface by a small dVol uniformally so that I can then compute: Vega = [Price(shifted surface) - Price(base surface)] / shift

And along the same lines I'd need to compute the second derivative (volga) and cross spot/vol derivative (vanna).

So far the only thing I've been able to find was to extract a constant vol from the surface for a vanilla option, and then reprice not with the whole surface but with a constantvol. => This only works for vanilla options and won't work for other products using the entire surface => This method is highly inefficient as it considerably slows down all pricing

Has anyone come across a more efficient method ? Is there a utility that shifts the entire surface at once ?

Thank you

Answer 1

There's no such utility in the library right now, but it can be written in a page or two of code.

It would work like, for instance, the SpreadedSwaptionVolatility works for swaption volatility; the idea is to write a class that inherits from the base BlackVolTermStructure class and takes the desired base volatility and spread.

Like SpreadedSwaptionVolatility, it would provide most of the required interface by delegating to the base volatility, as in

inline DayCounter SpreadedSwaptionVolatility::dayCounter() const {
    return baseVol_->dayCounter();
}

while the methods returning the volatility would be implemented as

Volatility SpreadedSwaptionVolatility::volatilityImpl(const Date& d,
                                                      const Period& p,
                                                      Rate strike) const {
    return baseVol_->volatility(d, p, strike, true) + spread_->value();
}

If you do write it, please consider contributing it to the library; if, instead, you're not familiar with C++, you can open an issue on the QuantLib GitHub repository and request the feature.