A non-Gaussian stochastic volatility model

Yuichi Nagahara, Genshiro Kitagawa

Abstract

ABSTRACT

A non-Gaussian stochastic volatility model is proposed in this paper. The model assumes that the time series is distributed as a Pearson type-VII distribution. The scale parameter of the distribution, which corresponds to the volatility of the process, is stochastic and is described by an autoregressive model with a constant term. Since the Pearson type-VII distribution can represent a broad class of distributions, including the normal distribution and t-distribution, the proposed model can be considered as a natural extension of the ordinary stochastic volatility model. For estimating the parameters of the stochastic volatility model, we apply a non-Gaussian filter. The model can be further generalized to the case where the shape parameter of the Pearson type-VII distribution is also time-varying. The usefulness of the model is demonstrated by the analysis of stock-return data, which suggests the relevance of the model to managing financial market risk.