Re: FiniteDifferences framework: composition of L including S

Posted by Luigi Ballabio-2 on
URL: http://quantlib.414.s1.nabble.com/FiniteDifferences-framework-composition-of-L-including-S-tp3348p3354.html

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