In this paper we consider several time-varying volatility and/or heavy-tailed models to explain the dynamics of return time series and to fit the volatility smile for exchange-traded options where the underlying is the main �Borsa Italiana� stock index. Given observed prices for the...

We consider time-changed Poisson processes, and derive the governing difference–differential equations (DDEs) for these processes. In particular, we consider the time-changed Poisson processes where the time-change is inverse Gaussian, or its hitting time process, and discuss the governing...