for the SABR modeldS=S y dW1dy=y alpha dW2dW1dW2=0,does anyone know how to prove that S is a martingale + whether S is U.I.?The pth moment of S_T is infinite for p>1, + any T>0thx

I believe that Jourdain "Loss of martingality in asset price models with lognormal stochastic volatility" shows it. In fact he proves a more general result: S is a martingale if and only if the correlation between the two brownians is less than or equal to 0.

Isn't it covered in our paper with Andersenhttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=559481otherwise a straightforward application of the "Sin" argument will prove it-V

I love that paper but I don't think Theorem 4.7 is justified (1/2<p<1 rho=0) (even tho it may be right)because when u make the transformation to a process with a Heston square root vol term, and use the comparison theorem, u need to know whether the kappa' and epsilon' parameters are such that the uth moment explodes(pg 27, the sentence that starts "By the choice of T in 4.11 ..." - what if no such T exists for the given kappa', epsilon' and u?saying that, given that kappa' =kappa q and epsilon'=epsilon q^{1/2},as q goes small i.e. as p->1 (SABR), then we do get the explosion

for rho=0 this should work as well. First use Tonelli to get integrability of S_{t}.Then to check E[S_t|F_s]=S_s, first condition S_t on sigma-alg. generated by W_stock up to s, and W_vol up to t,and use independence.