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Re: SABR model

Posted by Luigi Ballabio on Nov 30, 2010; 4:30pm
URL: http://quantlib.414.s1.nabble.com/SABR-model-tp265p267.html

On Thu, 2010-11-25 at 20:09 -0800, spz wrote:
> I think it was a tiny bug in the implementation. It should be a Taylor
> expansion about z = 0 (when close to ATM, z is close to 0 ). I did the
> expansion, and found the following formula
>
> z/xx ~ 1 - 0.5*rho*z + (3*rho*rho + 6*rho + 2)/12*z*z
>
> The difference of this one and the one in the implementation is
> 0.5*rho*rho/(1-rho)*z in leading order. Actually, when z is small ( z*z <
> QL_EPSILON*10 ), this difference doesn't matter

True, but I'd prefer to have a correct expansion rather than a wrong one
which is close enough.  May you double-check the expansion and provide a
patch for the file?

Thanks,
        Luigi


--

Weiler's Law:
Nothing is impossible for the man who doesn't have to
do it himself.



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