Comparative Study of Two Extensions of Heston Stochastic Volatility Model

In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and calibration of implied volatility is the addition of a few other factors to the volatility process. This paper contemplates two extensions of the Heston stochastic volatility model. Out of which, one considers the addition of jumps to the stock price process (a stochastic volatility jump diffusion model) and another considers an additional stochastic volatility factor varying at a different time scale (a multiscale stochastic volatility model). An empirical analysis is carried out on the market data of options with different strike prices and maturities, to compare the pricing performance of these models and to capture their implied volatility fit. The unknown parameters of these models are calibrated using the non-linear least square optimization. It has been found that the multiscale stochastic volatility model performs better than the Heston stochastic volatility model and the stochastic volatility jump diffusion model for the data set under consideration.