I am trying to calibrate parameters from market data using variance gamma (VG) or CGMY model on daily base for few years.Considering speed and accuracy, which optimization method is the best?Thanks

What kind of calibration?

calibration to options priceQuoteOriginally posted by: Marco72What kind of calibration?

I would use Differential evolution and Fourier pricing, using the preferred integration contour [$]\Im z = \frac{1}{2}[$] discussed in my "A Simple Option Formula ..." paper -- available here. Once I got it working with a robust Fourier integrator, to increase the speed I would move to a caching method like Fang & Oosterlee's COS method. I work in Mathematica, where this optimization method is an option to NMinimize. You can google the docs online for details of that. Presumably, it could be set up more or less the same way in Matlab, or other systems. Some related experiments with the VG model are reported by Itkin here

Thanks, Alan!New to Differential Evolution.Not quite understand the crossover part.What does the condition mean? Why is that? What is the intuition behind this condition?if [$]rand_j(0,1)\leq CR[$] or [$]j = j_{rand}[$] QuoteOriginally posted by: AlanI would use Differential evolution and Fourier pricing, using the preferred integration contour [$]\Im z = \frac{1}{2}[$] discussed in my "A Simple Option Formula ..." paper -- available here. Once I got it working with a robust Fourier integrator, to increase the speed I would move to a caching method like Fang & Oosterlee's COS method. I work in Mathematica, where this optimization method is an option to NMinimize. You can google the docs online for details of that. Presumably, it could be set up more or less the same way in Matlab, or other systems. Some related experiments with the VG model are reported by Itkin here

You're welcome. Re your question, I have no clue -- I treat Mathematica's implementation of DE as a black box!

DE is explained well herehttp://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.9696The authors have written a book as well.A minimal DE would consist of ~30 lines of code. //!! BTW I see red-lined Maths ERRORS in the posts below!!

I would use (and have used) Fourier inversion of the characteristic function for pricing. For VG and CGMY with Y parameter close to 0, I would recommend using the "parabolic iFT" of Boyarchenko and Levendorskii (see here and here). For the optimisation algorithm, I tend to use Matlab's fminsearch, with some tweaks.