Sequential Monte Carlo for fractional stochastic volatility models |
| |
Authors: | Alexandra Chronopoulou Konstantinos Spiliopoulos |
| |
Institution: | 1. Department of Industrial &2. Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA.;3. Department of Mathematics and Statistics, Boston University, Boston, MA, USA. |
| |
Abstract: | In this paper, we consider a fractional stochastic volatility model, that is a model in which the volatility may exhibit a long-range dependent or a rough/antipersistent behaviour. We propose a dynamic sequential Monte Carlo methodology that is applicable to both long memory and antipersistent processes in order to estimate the volatility as well as the unknown parameters of the model. We establish a central limit theorem for the state and parameter filters and we study asymptotic properties (consistency and asymptotic normality) for the filter. We illustrate our results with a simulation study and we apply our method to estimate the volatility and the parameters of a long-range dependent model for S& P 500 data. |
| |
Keywords: | Long memory stochastic volatility Rough stochastic volatility Parameter estimation Particle filtering |
|
|