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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).

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