  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.
