Modelling Stochastic Volatility with Leverage and Jumps: A Simulated Maximum Likelihood Approach via Particle Filtering

S. Malik and M. K. Pitt

Working papers from Banque de France

Abstract: In this paper we provide a unified methodology for conducting likelihood-based inference on the unknown parameters of a general class of discrete-time stochastic volatility (SV) models, characterized by both a leverage effect and jumps in returns. Given the nonlinear/non-Gaussian state-space form, approximating the likelihood for the parameters is conducted with output generated by the particle filter. Methods are employed to ensure that the approximating likelihood is continuous as a function of the unknown parameters thus enabling the use of standard Newton-Raphson type maximization algorithms. Our approach is robust and efficient relative to alternative Markov Chain Monte Carlo schemes employed in such contexts. In addition it provides a feasible basis for undertaking the nontrivial task of model comparison. Furthermore, we introduce new volatility model, namely SV-GARCH which attempts to bridge the gap between GARCH and stochastic volatility specifications. In nesting the standard GARCH model as a special case, it has the attractive feature of inheriting the same unconditional properties of the standard GARCH model but being conditionally heavier-tailed; thus more robust to outliers. It is demonstrated how this model can be estimated using the described methodology. The technique is applied to daily returns data for S&P 500 stock price index for various spans. In assessing the relative performance of SV with leverage and jumps and nested specifications, we find strong evidence in favour of a including leverage effect and jumps when modelling stochastic volatility. Additionally, we find very encouraging results for SV-GARCH in terms of predictive ability which is comparable to the other models considered.

Keywords: Stochastic volatility; Particle filter; Simulation; State space; Leverage effect; Jumps. (search for similar items in EconPapers)
JEL-codes: C01 C11 C14 C15 C32 E32 (search for similar items in EconPapers)
Pages: 50 pages
Date: 2011
New Economics Papers: this item is included in nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:bfr:banfra:318

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