Hi all, for my study I am doing a project where I have to study the convergence rate of a Euler scheme for a SDE driven by a levy process. This a very simple one, namely:dS/S = dZwhere Z is a Levy process of infinite activity. I have to do that for different Levy measures, and compute the price of a call optionE(h(S_T))This is why I was wondering if there exist closed form formulae available for some Levy measure ?thank you very much!

QuoteOriginally posted by: AlekkHi all, for my study I am doing a project where I have to study the convergence rate of a Euler scheme for a SDE driven by a levy process. This a very simple one, namely:dS/S = dZwhere Z is a Levy process of infinite activity. I have to do that for different Levy measures, and compute the price of a call optionE(h(S_T))This is why I was wondering if there exist closed form formulae available for some Levy measure ?thank you very much!yes, for instance variance gamma process (see Madan, Carr, and Chang 1998), double exponential jump diffusion (see Kou 2002). There might be many others, but I only come across these two.

depends what you mean by closed form - VG typically uses numerical integration and DEJD uses inversion of Laplace transform - though values are quick and accurate they're not as simple as say the Black-Scholes formula

Black-Scholes formula uses numerical integration, as well.

You should have a look at the two books :- Cont, Tankov- Schoutens