Title: Historical and risk-neutral estimation in a two factors stochastic volatility model for oil markets

Authors: Gaetano Fileccia; Carlo Sgarra

Addresses: Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo Da Vinci, 32-20133 Milano, Italy ' Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo Da Vinci, 32-20133 Milano, Italy

Abstract: In this paper, we analyse spot prices and futures quotations to get inference in the crude oil market. Data are referred to West Texas Intermediate (WTI) index which tracks the crude oil barrel price on New York Mercantile Exchange market. While big part of statistical research in finance deals with risk neutral modelling or with modelling under the historical measure, the purpose of the present paper is to estimate the parameters of three different models when their dynamics is described under both measures. In order to perform this estimation, we resort to a recent technique in Bayesian inference: the particle Markov Chain Monte Carlo (PMCMC) proposed by Andrieu et al. (2010), in which particle filters (PF) algorithms are used to estimate the marginal likelihood for MCMC inference. We adopt a stochastic volatility two-factor framework to describe the spot price dynamics, by extending a previous model proposed by Yan (2002).

Keywords: PMCMC; particle MCMC; Markov Chain Monte Carlo; Bayesian estimation; commodity markets; energy markets; stochastic volatility; models with jumps; historical estimation; risk-neutral estimation; crude oil markets; spot prices; futures quotations; modelling; particle filters; price dynamics; oil prices.

DOI: 10.1504/IJCEE.2015.072289

International Journal of Computational Economics and Econometrics, 2015 Vol.5 No.4, pp.451 - 479

Received: 29 Aug 2013
Accepted: 17 Sep 2014
Published online: 08 Oct 2015 *

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