Narrow Results

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility (TC-FMR-SV) models. Using spectral theory and singular perturbation techniques, we derive an approximation for the price of any European option in the TC-FMR-SV setting. Three examples of random time-changes are provided and are shown to induce distinct implied volatility surfaces. The key features of the TC-FMR-SV framework are that (i) it is able to incorporate jumps into the price process of the underlying asset (ii) it allows for the leverage effect and (iii) it can accommodate multiple factors of volatility, which operate on different time-scales.

This paper studies a stochastic conditional duration model running on multiple time scales with the aim of better capturing the dynamics of a duration process of financial transaction data. New Markov chain Monte Carlo (MCMC) algorithms are developed for the model under three distributional assumptions about the innovation of the measurement equation for a two-component model. Simulation results suggest that the proposed model and MCMC method improve in-sample fits and duration forecasts. Most importantly applications to FIAT and IBM duration datasets indicate the existence of at least two factors (or components) governing the dynamics of the financial duration process.