http://quantlib.414.s1.nabble.com/FiniteDifferences-framework-composition-of-L-including-S-tp3348p3350.html
Do you know that this centred difference scheme gives terrible approximations to the delta and gamma at the strike price? See the references below.
Daniel J. Duffy
> -----Original Message-----
> From:
[hidden email]
> [mailto:
[hidden email]]On Behalf Of Luigi
> Ballabio
> Sent: 11 October 2004 11:48
> To: Penschke, Walter
> Cc:
[hidden email]
> Subject: Re: [Quantlib-users] FiniteDifferences framework: composition
> of L including S
>
>
> On 2004.09.23 15:08, Penschke, Walter wrote:
> > Hello QL-community,
> >
> > I did have a look at the finite differences framework of
> QL. The sample
> > code provided in the documentation is based on a version of the
> > BlackScholes differential equation, which is defined for log(S).
> >
> > I was now trying to perform similar calculations as in the example,
> > however now based on the BlackScholes differential equation
> for S. I.e.:
> > the differential equation looks like this:
> >
> > f = f(S, t)
> > df/dt = rf - rS df/dS - 1/2 sigma^2 S^2 d^2/dS^2
> >
> > (For the sake of simplicity I skipped the dividend yield in
> the above
> > formula.) I now wonder, how I should set up the
> differential operator L
> > with the tools provided by QL. Especially it is not clear
> to me how I
> > should incorporate S in the definition of the differential
> operator L.
>
> Walter,
> sorry for the delay. As there's more math in the answer
> than plain
> e-mail can carry, I'm writing it in LaTeX and attaching it to
> this mail.
>
> Later,
> Luigi
>
>
>