A spectral estimation of tempered stable stochastic volatility models and option pricing

This paper considers alternative option pricing models and their estimation. The stock price dynamics is modeled by taking into account both stochastic volatility and jumps. Jumps are captured by the tempered stable process and stochastic volatility is introduced via time changing the stochastic processes. We propose a characteristic function based iterative estimation method, which overcomes the problem of non-tractable probability density functions of the models and facilitates computation. Estimation results and option pricing performance indicate that the infinite activity stochastic volatility model dominates the finite activity model. We also provide an extension to investigate the double-jump model by introducing jumps in the variance rate process.