Dear all. For an option market maker, I need to fit an implied volatility surface. If I well understand, the procedure is like this: 1.using the BS(inverse) to calculate the implied volatility 2.using the implied volatility data to fit a model, for example Gatheral's SVI model. 3.using the model to trade the option. 4.for example, every 5 mintues to update the parameter of the fitting model. my question is, but our books tell us that the BS model is wrong ? then we use the wrong model to fit another one, then we get a wrong fitting ? I am confused. Many thanks.

"Implied vol" is nothing but a convoluted way to quote market price. You are not really "using" B-S model in your case. You might have skipped using B-S at all if you fit your favorite SVI model directly to market price instead of market implied vol.

but for fitting my favorite SVI model, I need some volatility data ? how Can I get it , if I don't use the BS model?QuoteOriginally posted by: secret2"Implied vol" is nothing but a convoluted way to quote market price. You are not really "using" B-S model in your case. You might have skipped using B-S at all if you fit your favorite SVI model directly to market price instead of market implied vol.

Take Heston as an example. You have the closed form Heston option price formula. You have market observed prices. You do the numerical fitting, it gives you the Heston parameters. Where has B-S vol come into play?

QuoteOriginally posted by: secret2Take Heston as an example. You have the closed form Heston option price formula. You have market observed prices. You do the numerical fitting, it gives you the Heston parameters. Where has B-S vol come into play?yes, taken heston as an example, it has the closed form of the option price, but it also has some parameters.for calculate the parameters, it needs to do the numerical fitting, for doing the fitting, I need to input the volatility, right ? where do I get the volatility ?

QuoteOriginally posted by: GuitarTraderQuoteOriginally posted by: secret2Take Heston as an example. You have the closed form Heston option price formula. You have market observed prices. You do the numerical fitting, it gives you the Heston parameters. Where has B-S vol come into play?...for doing the fitting, I need to input the volatility, right ? where do I get the volatility ?Where to get WHAT volatility? Under Heston, the instantaneous variance (hence volatility) is a stochastic process. It is no implied vol, and doesn't require being input from elsewhere. Please make sure you understand what implied volatility is.

The heston model:http://en.wikipedia.org/wiki/Heston_modelξ is the vol of vol,the instantaneous variance (hence volatility) is a stochastic process, yes, it doesn't need to input the vol of vol ?QuoteOriginally posted by: secret2QuoteOriginally posted by: GuitarTraderQuoteOriginally posted by: secret2Take Heston as an example. You have the closed form Heston option price formula. You have market observed prices. You do the numerical fitting, it gives you the Heston parameters. Where has B-S vol come into play?...for doing the fitting, I need to input the volatility, right ? where do I get the volatility ?Where to get WHAT volatility? Under Heston, the instantaneous variance (hence volatility) is a stochastic process. It is no implied vol, and doesn't require being input from elsewhere. Please make sure you understand what implied volatility is.

as has been mentioned, black scholes implied vol is just a way of expressing option prices. You can fit your heston model to the prices or to the implied vols. If you match prices you match vols. They're equivalent.

I think OP is talking about vol of vol, in which case the answer to the question would be, it is a calibration output instead of input.