chika, I have tried Kou's version as well, but the results are exactly[\i] the same!actually, I have tested the GS algorithm quite extensively, but it never worked perfectly even for simple function, linear or whatever. what I observed is that initially it converges to the actual value, but then it becomes overflow and diverges. do you get some different behaviour??anton

>I have tried Kou's version as well, but the results are exactly the same!Nevertheless, I assume that the second term has to be accounted for. You use quite large theta1. Recall that the second root beta2>theta1. In your example theta1=12.6 so that the second term with exp(-beta2*x)<exp(-theta1*x) \sim 0 (x>0). Compare your formula with Kou's one for smaller values of theta and smaller time.I use Stehfest algorithm (Gaver-Stehfest is a modification of it). The algorithm is very reliable and accurate.

I use Stehfest algorithm (Gaver-Stehfest is a modification of it). The algorithm is very reliable and accurate.I have only experimented with the Gaver-Stehfest. Can you give me reference or source code for the Stehfest algorithm? I have read the original paper and Stehfest mention such type of problems. regards, Anton

Thanks, Anton, for posting your talk, which was informative.With regard to exponential jumps vs. Merton's model, bothyou and Chika like the exponential but your applications are both differentthan mine.I think a good "non-parametric" study is needed if someone hasn'talready done it. If anyone is looking fora good research project, it would be very valuable to take the short-datedoptions of say the SPX, and fit the smile to a jump-diffusion of a verygeneral sort. This general model would have jump-probabilites p_i to be determined for jumps to bins (x_i, x_i+1). The number ofbins could be 10, for example.My guess is that for the SPX, the max. fitted probability would beto a negative bin, ruling out the single or (zero-centered) double exponential. But I am certainly willing to be shown otherwise.Regards,alan

If you know the math, you should find the tangent vector bundle for the diffusion at hand. These vectorsare the streamlines (iso-probability lines). Barriers just remove the probabilities between streamlines (waterfalls).Get it?