Hi,I'm trying to find the characteristic function for the CEV model - does anyone know where to find it? (tried google quite a bit...)Thanks!

It is very possible that you will not get a closed form formula but you can get Kolmogorov equation for it.

I do not think you can get any closed form for it.Best,

Since the pdf of S is known, I would just define it as an integral which you do numerically and declare victory. p.s. Thinking some more, maybe there is hope; if you can reduce it toint(0,infy) x^a e^(-x) BesselI[nu, b Sqrt[x]] dx, with general (a,b, nu), then that one is doable in terms of special functions. Here BesselI[ , ] is the modified Bessel function.So, suggest you re-post your question as one about a nicely latexed integral. [also, see my follow-up below]

Thanks Alan. I was thinking of whether it is feasible to use the Fourier transform pricing approach from your paper on it. Looks like even if I find an expression for the characteristic function, it may be quite slow to evaluate. I'll perhaps come back to this at a later point, as it is an interesting problem.Thanks again to all who answered.

It's indeed possible. It's overkill for the CEV model, but quite useful for CEV-SV model(s), say SABR.The trick is to write the asset sde as dS = r S(t) dt + sigeff(t) S(t) dW1, where sigeff(t) = alpha(t) S(t)^(beta-1) is an "effective" log-normal volatility. Then develop the sde for sigeff(t) and then follow the recipes in my book I.For SABR (with drift above), one has d alpha(t) = nu alpha(t) dW2.This leads to a "standard" sde pair for {S(t),sigeff(t)}, and so option values are given by standard formulas in termsof the conditional char. function of log S. As an approach to SABR, I have quite a bit of elaboration on this in my book II (forthcoming, hopefully 2012). [There are a number of related discussions on this forum with "oislah", whohas developed some of this method also, for SABR. Use the forum search function with 'SABR' in the title]If alpha(t) is a constant, then you have the ordinary CEV model. Carrying out this prescriptionleads to the 3/2-SV model [a fact that was originally noted by Steve Heston]. This is discussed (with r=0) on pg 305 of "Option valuation under stochastic volatility". But, as I said, this approach is somewhat overkill for that one ...