Dear all,We have also been working on a stochastic volatility project. We want to calibrate Heston model for fx options.We wanted to use ASA for calibration.Sergei Mikhailov, Ulrich Nögel state in their paper 'Heston’s Stochastic Volatility,Model Implementation,Calibration and Some Extensions' that 'In contrast to the local optimizers the initial guess is (hopefully)irrelevant in the concept of stochastic optimization.' And they use ASA for calibration.When we try to calibrate Heston model with ASA using a data set which consists of 42 options on a spesific day we see that calibration results totaly depend on initial parameters.Further although we get different calibrated values ,these different set ofparameters equally work well,we have very minor errors for each of them.We wonder where the problem is.Can it be something related to number of datapoints i.e should we take e.g 84 options on that day in stead of 42 options?We want look at the term structure of parameters then how can we achieve this if there are 2 different set of parameters which work equally well for a spesific day.I mean how can we handle with that multiplicity problem?Thank you very much for your help.

Here are some points about calibration :- You should first try and calibrate to a single smile (but to many points, like 16) : for a classical smooth shape, you are supposed to be able to fit perfectly the smile with the Heston model, and even, there will be different sets of solutions possible !Then you could go up to 2 or 3 maturities, and you will see quickly the limitations of the model !- LM seems obvisously faster than a less constraigning simplex method, but I don't have the quantitative answer for that...I think we can't calculate the derivatives analytically, I used a discrete LM..- If you calibrate to several maturities, you shouldn't obtain different sets of parameters possibles.However, if so, I don't see the problem, just choose the one implying the most plausible dynamics... the trick then will be to recalibrate from this set of parameters not to jump from a point to another in the space of parameters..

Thank you very much g000RRRr.Actually,we haven’t tried to calibrate Heston model to a single expiration yet but what we did is exactly what you suggest.We used 6 options(3 ITM,1 ATM,3 OTM) for each 1 month,2 m ,3 m ,6 m,9m ,and 1 year expirations in total 42 options data on 16 January 2008.When we try to calibrate the model using this data we obtain (for now at least) 3 different set of parameters which work equally well( sum of error squares is approximately %0.002 for each of them.) as we change intial parameters.For example we have:Solution =[kappa theta sigma rho V0]Solution =[ 0.2656 0.1057 0.2304 0.9997 0.0186 ];Solution =[5.2404 0.0273 0.3836 0.9971 0.0178];Solution = [1.4336 0.0430 0.3482 0.8176 0.0182];Also since ASA(as they claim ) is a global optimizer it shouldn’t depend on the initial values.We don’t know e.g which kappa to choose as the kappa for 16 January 2008.For example if I find kappa as ‘5 ‘ for 17 January 2008 and choose 5.2404 for 16 January 2008 then I could say the kappa is stationary but If I take kappa as 0.26 for 16 January 2008 then I could say kappa is not stationary.Thank you very much again for answers.best regards,

ASA is not a perfect global optimizer, it can miss the global optimum...The only way to do a global optimization is to go through the whole space of parameters actually...Wether you use one value or another for your kappa, you can find it approximately stationary : just recalibrate with a local optimizer !But I'm wondering .. what market are you monitoring ?'Cause it's just impossible to get such good results calibrating Heston on 6 short maturities : on index options, you should have errors of about 1 vol point or more, I would say.

Is it true that there is no global optimizer for non-linear system? If so, what is the best technique to find "global" extremum using local optimizer? I only know the technique of trying many different starting points and find the best among them. Are there better technique?

weight vega??Does it mean that the vega*(actual price - model price)???

weight vega??Does it mean that the vega*(actual price - model price)???

Just read the thread, it's all there