Re: [Quantlib-dev] LocalvolSurface.cpp

[Ferdinando A. <qf...@am...>]

Hi Michael

> i recently did a lot of testing with the localvolSurface class (which
> contains Gatherals Dupire Formula) and i am not very happy with the results.
> Ok, the class is (regarding to the documentation) untested, so I guess I
> cant expect it to work properly.

Last week Klaus fixed time derivative (now performed at constant
moneyness instead of constant strike) and added tests.

> But I figured that numerical problems cause
> this class to return the error message “negative local vol …  the black vol
> surface is not smooth enough”. [...]
> the problem lies in the second derivative of the
> black variance with respect to the strike.

you are right. I will fix it, probably moving time/strike (numerical)
derivatives in the BlackVolTermStructure base interface, allowing for
overloading in derived classes which might provide exact derivatives.

BTW I have a related question. Black ATM variance must be increasing
in time; I've always taken for granted that this is also true for
every (not just ATM) constant moneyness section of the Black surface.
Is this a non-arbitrage result or shaky common sense?

ciao -- Nando