A very basic question: For the levy models (not jump diffusion ones) like variance gamma (VG), NIG, CGMY, meixmer etc., only the VG models have closed form option formulas. For all the remaining models are we basically expected to work with the characteristic functions and numerically integrate?

The NIG has closed-form pdf too. In the paper below it is applied to fit the smile of inflation options as an alternative to SABR.http://papers.ssrn.com/sol3/papers.cfm? ... id=1968453

thanks. i had actually meant close form option formulas, but i guess close form pdf is almost as good. any other Levy models with close-form option formulas?

You are probably right. I would argue, however, that the characteristic function approach is more straightforward to implement than the "closed-form" VG formula (loads of horrible special functions to evaluate).

the so-called closed-form VG option price that you refer to contains some of the more difficult Bessel functions - so for practical purposes, it's much easier to compute the option price as a numerical integral of modified Black-Scholes prices

QuoteOriginally posted by: ehYou are probably right. I would argue, however, that the characteristic function approach is more straightforward to implement than the "closed-form" VG formula (loads of horrible special functions to evaluate).Another approach (in C++) is to use modified Bessel of 2nd kind and gamma functions in the awesome formula for VG option price. What is then left is the degenerate hypergeometric function for which there is nothing in Boost but it is a combination of gamma and a benign integral; the latter can be computed with a rough-and-ready quadrature method. A rough guess is it would take < 2 hours and debug to get it working.Unfortunately, there is no Quadrature library in Boost at this moment. //SSRN down, so can't check NIG closed solution, but its pdf is easy to compute.

QuoteSSRN down, so can't check NIG closed solution, but its pdf is easy to compute.They use a quadrature to compute the option prices.

Thanks for the insights. The VG option formula indeed looks quite intricate and the derivation even more cumbersome. I found it quite interesting that from the time Madan and Seneta published the first paper on Variance Gamma in 1990 (perhaps available as a working paper much before that), it took 8 years before Madan, Carr and Chang published the option pricing formulas in 1998. Pretty impressive work I would say.

I am a PhD student working on a new class of pdf?s denoted 2-EPT probability density functions with applications in Financial Modelling. This class corresponds to those pdf?s with a rational characteristic functions e.g. Variance Gamma (VG) under the parameter restriction that the input parameter ?C? is integer. Assuming this constraint we obtain straightforward closed form option prices when the asset follows a VG process. Expressions for delta and gamma are also available although I am unsure of how useful these quantities are in the context of a pure jump process? We are currently working on necessary and sufficient conditions for a random variable with rational characteristic function to be infinitely divisible and to determine its levy measure. Draft version will appear shortly.I?ve recently created a website to make the work accessible www.2-ept.com. The link to a paper which may be useful for readers of this topic is here and see section 3I post here regularly under a different username....