Sequential Monte Carlo for fractional stochastic volatility models

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

AMS Subject Classifications:

• C13
• C15
• C22
• C32
• C63

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research of A.C. supported in part by a start-up fund from the University of Illinois at Urbana-Champaign and by the Simons Foundation [grant number 319216]. Research of K.S. supported in part by a start-up fund from Boston University and by the National Science Foundation [DMS 1550918].