I'm doing Heston and VG calibration with option market data. My question is: could it be useful to have bounds on the values that parameter can be assumed? e.g.: for \sigma parameter in VG model impose that 0<\sigma<70%...

my experience is you do not have to do that with VG (but you have to make \sigma in VG to be positive for sure). the optimization coverges fairly fast. i tried a few reasonable initial values and got the same optimal parameter set in the end. good luck

Hi Fei,Could you please elaborate a bit more. I am new to structuring. the calibration stuff is new to me...please elborate..regardscosmo

It also depends on the optimization algorithm you use. Setting bounds might increase the calibration speed.

Can i accept any value for model parameters from calibration (provided that the objective function has a low value)?e.g.: if i calibrate VG model with option market data and i obtain a value for parameters (\theta,\sigma,\nu)=(4,5,7) and value for obj. function = 0.001, is this solution better than (\theta,\sigma,\nu)=(-0.2,0.30,0.03) and obj. function=0.02 even if (\theta,\sigma,\nu)=(4,5,7) have no mean (\sigma is the volatility of Brownian motion and a value for \sigma=5 means a 500% volatility! ).My doubt is that with option market calibration i obtain the "risk-neutral" parameters and so i don't know if it's right give them a "real" mean...(a 30% volatility is fair )

hi hoare,do you really get (4, 5, 7) with a obj value less than (-0.2, 0.3, 0.03)? my experience is, at least for VG, that i got the same parameter set, say (-0.2, 0.3, 0.03), no matter what initial values i started with. i might be wrong, but you are right (4, 5, 7) makes no sense at all. btw, are you using carr and madan FFT approach?

Bingfei, i don't get (4,5,7) values! It was an example...I'm using the Fractional FT approach .Which optimization algorithm you' re using? Anyway, my doubt remain:QuoteMy doubt is that with option market calibration i obtain the "risk-neutral" parameters and so i don't know if it's right give them a "real" mean...(a 30% volatility is fair [\q]

i coded it in c++ and the package i borrowed was developed at sandia laboratory called opt++. one of its routines calles quasi-newton method while using finite difference to estimate the Jacobian. it worked pretty well ... regarding your doubt, it is possible you found only local min not global one. whether you call it "risk neutral parameters with a real meaning" is not so important, given the problem is only up to the issue of local/global mins. there is an FRFT matlab code for VG calibration online somewhere on this board, maybe you can use it to compare with yours, if your wrote your own.