Spectral Iterative Estimation of Tempered Stable Stochastic Volatility Models and Option Pricing

This paper addresses alternative option pricing models and their estimation. The stock price dynamics is modeled by taking into account both stochastic volatility and jumps. Jumps are mimiced by the tempered stable process and stochastic volatility is introduced by time changing the stochastic process. We propose a characteristic function based iterative estimation method, which overcomes the problem of nontractable probability density functions of our models and eases computational difficulty related to other methods. The estimation results and option pricing performance indicate that the infinite activity stochastic volatility model is more preferrable than the finite activity model. We also make an extension to investigate double-jump model by introducing jumps in the variance rate process.