HiI try to calibrate heston model to implied volatility surfaces. To do that, i use genetic algorithm with SSE weighted by vega BS.I solve the fourier transform with numerical integration (gauss legendre) and the characteristic function is the gatheral formula.The absolute error is over 1.5 volatility points for long maturities. Do you think that gatheral formula is not sufficient and i must used the the kahl method to solve the complex logarithm issue and lobatto quadrature ?Could you help me on this subject ?Thanks

as in many posts already indicated: please have a look at The Little Heston Trap.Maybe also good to know is that the formual was already around long time - so refering to it as the Gatheral formula is not really that appropriate.

Wim,Can you elaborate on the history of that variation?regards,

The formula was already in the paper by Bakshi-Cao-Chen "Empirical Performance of Alternative Option Pricing Models", Journal of Finance, Vol. LII, No. 5, december 1997, pp. 2003-2049. More precisely, you find it in Equation (A.11);

Thanks, I see it. Good eye. I guess there is a 50/50 chance of getting it, if you aren't looking for it.

about calibration I found that the most used minimization function is linear in the number of options used and parabolic in the absolute error :SUM ( weight * ( heston_price - mid_price ) ^ 2 )I think that giving error at prices within the bid-ask spread is not correct and I'm trying another minimization function, such as:SUM ( weight * ( heston_price - ask ) ^ 2 ) or SUM ( weight * ( heston_price - bid ) ^ 2 ) when price is out of the range and 0 elsewhere.does anybody have other suggestions or ideas???

Alternatively, if you want to take into account the bid ask spread, you can use the mid-price of the option but accept a parameter set, where bid /ask are the bid/ask prices quoted on the market. This means that you will not require the model to match the mid exactly, but fall, on average, within the bid-offer spread :SUM ( weight * ( heston_price - mid_price ) ^ 2 ) =< SUM ( weight * ( bid_price - ask_price ) ^ 2 ) Regards.

and what about the idea of using the power 4 ???SUM ( weight * ( heston_price - mid_price ) ^ 4 ) this is still an even error function with continuous derivatives but it may give more importance to prices out of the bid-ask range...QuoteOriginally posted by: quantmanAlternatively, if you want to take into account the bid ask spread, you can use the mid-price of the option but accept a parameter set, where bid /ask are the bid/ask prices quoted on the market. This means that you will not require the model to match the mid exactly, but fall, on average, within the bid-offer spread :SUM ( weight * ( heston_price - mid_price ) ^ 2 ) =< SUM ( weight * ( bid_price - ask_price ) ^ 2 ) Regards.

I have a question on heston calibration.1. Can one calibrate Heston by fixing the mean reversion speed parameter.Since we know that the price depend on the ratio mean reversion speed over the volatility of the volatility, the initial vol et the long term vol.In my opinion we can not calibrate the model.2. Let consider the BGM model belowWe have the same question can we calibrate this model by fixing kappa.I think yes. I want to know if my answer are wrong.Thanks

Theoretically speaking, I don't think you can. And you mentioned the very reason. More specificaly, you might want to ave a look at a paper by Daniel Dufresne, called "The integrated square root process"In it, Dufresne points out the fact, that all the moments of the Heston diffusion (which can also be seen by a scaling in the dynamics) only depend on the ratio, the initial vol and the long-term variance., never on the mean-reversion speed alone.I'm not sure for BGM, I don't really know it.

Thanks,