Stochastic volatility models are calibrated to the prices of equity options and compared along different dimensions, both internally across calibration results and externally against observable market factors. The aim is to identify which of the competing models available in academic literature, if any, can be said to be significantly better for pricing purposes.
The study shows that the most popular model, the Heston model, seems to be the best when compared to real market conditions, while other models are less accurate seemingly due to their inbuilt instability. While comparing the models across calibration parameters, no clear distinction can be made with regards to the superiority of any of the models due to noise in the calibration process.
It will also be demonstrated how problems relating to the stochastic volatility models in general affect results and the fit to market prices and we will make some considerations about the appropriateness of stochastic volatility models in general. We demonstrate how the models are able to replicate the kurtosis seen in market returns, but that their inability to model large negative returns while still maintaining symmetry on the upside make the models unable to price calls with certain strikes and maturities.