Hello all together,my question comes from the financial mathematics sector (pricing barrier options) but I am sure that you are the experts for this.I am trying to invert the following construct (equation 4.3/4.4 in http://laurent.nguyenngoc.free.fr/data/options-levy.pdf):Int(0,INF)exp(-q*T)dT Int(-INF,INF)exp(i*u*k)dk Int(0,INF)exp(-v*h)dh f(T,k,h) This is a combination of a laplace transform, a fourier transform and a laplace transform. I tried to find an algorithm which can inverse all these three transforms together but I was not able to find anything for this case. So now I think I have to invert separaetely the laplace transform, then the fourier transform and finally the second laplace transform sep by step. Do you agree?On the right hand side of the equation is a very ugly and long expression with complex numbers and fractions (can be seen via the link) where I need to have an algorihtm which can handle with such a structure. Be careful that on the right hand side is a typo but this does not change the structure; the right hand side without typo is the following:It would be great if anyone knows such an algorithm and could give me a hint. An answer would be a great support as this question did cost me a lot of nerves and time!Thanks very much in advance and best regards from Bavaria,Andrea

Take a look at this thesis by G. CardiBefore getting carried away, you should reduce the problem to the minimum number of integrations.If you are doing a single barrier option with a spectrally one-sided Levy process, you can probablyreduce the setup to inverting some f(q,z) where q is a Laplace variable and z is a Fourier variable.Even better, often the Fourier inversion of f(q,z) can be done by residues, which only requires aroot search in the complex z-plane. The net result is that you only have one inversion, a Laplaceinversion: this kind of reduction should be your first goal before numerics. (Personally, my patience runsout at two inversions, so I have never attempted three!).I have various articles in Wilmott magazine on all this -- see the thesis for cites.

Thanks for the answer but unfortunately, I think I can't reduce the integrals to just two integrals. And if this should be the case I have the same problem that I need special laplace inverse and fourier inverse algorithms to get the original function.Help still welcome!

why are you bothering with this paper at all - it's all theory and continuous sampling cases are much less relevant than discrete sampling cases?

I am bothering with this because it is part of my (theoretical!) master thesis, so it's not my choice! But do you have an idea??

I just can't see the benefits from this paper - there are alternative approaches that rely on a single fourier or laplace inversion to value such options, even in the levy world - so I'd be looking at those alternative approaches

Thanks for this interesting news. I did not know that although I did a lot of research in this topic during the last two months. Could you please give me a hint where (which author..) I can find these approaches? Thanks a lot in advance

well, i hv no idea but interest abt the topicjust wanna help up this post to wait for the good tips