yep mib... don't you find interesting to determine the vol of vol, or the speed kappa from your implied vol model..at least, my options desk is interested in

je ne suis pas sur qui est une blonde ici mais...There is no such thing as "vol of vol determined by an implied vol model". The problem is that vol of vol describes dynamics of the underlying movements and the shape of the smile can be determined by many different factors. For example, for a fixed maturity, one can get any smile shape one wants by simply assuming a funny return distribution for this horizon. May be I not quite getting what you mean by an "implied vol model".If a guy on your desk wants to take a 90%/100%/110% butterfly position and wonders at which Heston-implied vol of vol level is he getting into it, he does not care about the global error of a least-squares fit. He cares about getting the curve shape right aroung the strikes he trades. It is easy to draw a reasonably shaped smile such that the least-squares optimal Heston fit will heavily misprice this butterfly.

Sorry mib but I don't agree !!!My question is just: With the implied surface, what is the value of the Heston or VG parameters. And why do I obtain different values when taking different starting values... So you don't answer the question, you just say that is a non-sense. No, my point is : kind you give a good algorithm to obtain the true gloabl min and did you have the same prob in the past ( it seems that you've never had such a prob because for you a local min is a min) I hope for you that your wife is a woman, and not an approximate woman (sorry for that bad joke...)

Well, by catching vol around ATM i mean fitting against vol (and to use that for pricing),so we are talking of the same thing here i think. But i do think that a neither a globaloptimum must exist nor that it is neccessary the best practical solution - simply if themodel is to far from data. A check around ATM is the easiest to be done first (i willupload an old skew where you can tell me what you would take for VG).Just an idea: instead of starting with constant vol you may approx the RND for eachexpiry and as the parameters are (analytical) related to excess kurtosis and skewnessof the distribution you can take an average to have a guess.But the main point is: you can not get a reasonable fit against an actual vol surface(error below 0.2 vol points vs the opinion of a desk), so a 'stable' local minimum isnot a bad thing.

The answers to your question are very simple:1)>"With the implied surface, what is the value of the Heston or VG parameters?" There are no Heston or VG parameters that would match your surface exactly in any 'global' metric. Depending on the metric chosen, the problem of fitting approximate Heston model parameters may be ill-posed or well-posed.2)>"And why do I obtain different values when taking different starting values?" Because the metric you use leads to an ill-posed problem. You can get all the optimizers you want but your optimization problem has miltiple local minima and which of them is global depends, among other things, on subtle properties of the algorithm you use to generate the vol surface, not on the market. With a good optimizer, you will find the global minima today, but tomorrow something will change a bit and the global minima will jump to another point.3) >"it seems that you've never had such a prob because for you a local min is a min". Where did you read that???Anyway, I give up. Good luck in finding the optimizer.

Hi SPAAGG,Did you find a solution to your question regarding the starting values to optimally calibrate the heston model to a given market volatility surface, I am doing something similar and it might help if we correspond offline, Here's my email: abhishekrajgarhia@yahoo.com. Please reply here or at my email if you wish to correspond/collaborate on this and other modeling projects.Thanks