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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433


TROSEL, Yeniree; HERNANDEZ, Aracelis  and  INFANTE, Saba. Estimation of stochastic volatility models via auxiliary particles filter. Rev. Mat [online]. 2019, vol.26, n.1, pp.45-81. ISSN 1409-2433.


The growing interest in the study of volatility for series of financial instruments leads us to propose a methodology based on the versatility of the Sequential Monte Carlo (SMC) methods for the estimation of the states of the general stochastic volatility model (GSVM). In this paper, we pro- posed a methodology based on the state space structure applying filtering techniques such as the auxiliary particles filter for estimating the underly- ing volatility of the system. Additionally, we proposed to use a Markov chain Monte Carlo (MCMC ) algorithm, such as is the Gibbs sampler for the estimation of the parameters. The methodology is illustrated through a series of returns of simulated data, and the series of returns correspond- ing to the Standard and Poor’s 500 price index (S&P 500) for the period 1995 2003. The results show that the proposed methodology allows to adequately explain the dynamics of volatility when there is an asymmet- ric response of this to a shock of a different sign, concluding that abrupt changes in returns correspond to high values in volatility.

Keywords : stochastic volatility models; space state models; auxiliary particles filter.

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