Hi people,I am currently trying to calibrate the heston model on the eurostoxx basing on Wilmott's Magazine Article: A perfect calibration! Now what?, using the ASA of Ingber.My heston is using the closed form solution with numerical integration. But I don't get enough good fits (some are less than 1% but a few of them, especially the OTM ones go up to 9%, I would like a better global fit for all options and a better one for the OTM) and for all, the optimizer doesn't converge on the same minimum value. I can understand that it can return different sets of parameters for the same cost function value (lot of local minimas) but returning really different cost function values...My cost function is actually the sum of squared errors. I've read about weighting it with the vegas but don't know how in pratical. I've tried to give it the best generated parameters of the previous test as startpoint to see how far it can converge to the minimum but at the third time, I get crazy results: the optimizer goes far away. Another point is the ASA itself, does anybody know a paper (excepted Ingber's one) that tells us how the optimizer is really working and how the tuning parameters affect the results?can anybody experienced help me about that?

If you use price differences then far ITM and OTM the options are close to their intrinsic values, and the differences are small. But small price differences in this area would translate into large implied volatility differences. Therefore normal price differences naturally put more weight ATM, as it is there that different parameters produce different results.You can try and minimize the implied volatility difference. I had good and bad experiences with that.Will weighting with vegas make any difference? It looks more or less like the pdf, so it would put less weight ITM/OTMBased on european vanilla options alone you dont get much information on the dynamic parameters of Heston, that is the speed of mean reversion and the vol-of-vol. Many different combinations will give you similar fit (there some sort of valley). If the optimizer runs away your integration might not be very robust for crazy parameter combination, or the optimizer might be crap. Use some global search, like GA or heuristics.Kyriakos

I guess it must have been your integration's problem, i.e., the truncation errors vary with maturity and strike.

thanks to both of you for your tips. I've changed my closed form solution, I'm using the more stable one, given in the "Little Heston Trap". About my integration, i'm using a preimplemented quadrature rule: gauss kronrod with 87 points on the interval [1e-7, 100], given in the Centerspace analysis package in C#. I compared my prices with the ones given in "Little Heston Trap", and get the same prices, so I suppose my pricer is now correct.For the weights with the vega, I don't know how to integrate them in my costfunction: should I use weights like vega/total vegas, or something like that?I just implemented the calibration with respect to implied volas and I'll try it this afternoon.Rez, could you tell me more about your calibration experience, since I don't have any. I'm just beginning quantitative studies...(2nd of Masters degree).analxyz:should I take a larger interval for the integration? up to 200?thanks a lot.

Calibrating with respect to implied volas give me now more stable results: my optimizer gives me stable results for a given cost function. And now, I'm concentrating on correcting my costfunction to get a better fit. I've tried weights with vegas/total vegas: the fit is usually better or equivalent except for the short maturity (2 weeks). So I tried with inversed weights to see if the fit would be better for the short maturitiy (because I'm putting more weight on it) and for the very short maturity and for deep ITM calls, the fit is better and gets worse with growing maturities and strikes.Is there a way to combine both approach to get a "tailored" fit?And I don't understand why the fit isn't better for OTM calls since their vegas is, like the ITM, small too. Shouldn't I make a calibration with only one type of moneyness, i.e., with ATM options separated, ITM options separated and then OTM options separated? And because Heston doens't fit well for short maturities, shouldn't I do the same for short maturities?