Abstract
In this article, an estimation methodology based on the sequential Monte Carlo algorithm is proposed, thatjointly estimate the states and parameters, the relationship between the prices of futures contracts and the spot prices of primary products is determined, the evolution of prices and the volatility of the historical data of the primary market (Gold and Soybean) are analyzed. Two stochastic models for an estimate the states and parameters are considered, the parameters and states describe physical measure (associated with the price) and risk-neutral measure (associated with the markets to futures), the price dynamics in the short-term through the reversion to the mean and volatility are determined, while that in the long term through markets to futures. Other characteristics such as seasonal patterns, price spikes, market dependent volatilities, and non-seasonality can also be observed. In the methodology, a parameter learning algorithm is used, specifically, three algorithms are proposed, that is the sequential Monte Carlo estimation (SMC) for state space modelswith unknown parameters: the first method is considered a particle filter that is based on the sampling algorithm of sequential importance with resampling (SISR). The second implemented method is the Storvik algorithm [19], the states and parameters of the posterior distribution are estimated that have supported in low-dimensional spaces, a sufficient statistics from the sample of the filtered distribution is considered. The third method is (PLS) Carvalho’s Particle Learning and Smoothing algorithm [31]. The cash prices of the contracts with future delivery dates are analyzed. The results indicate postponement of payment, the future prices on different maturity dates with the spot price are highly correlated. Likewise, the contracts with a delivery date for the last periods of the year 2017, the spot price lower than the prices of the contracts with expiration date for 12 and 24 months is found, opposite occurs in the contracts with expiration date for 1 and 6 months.
Highlights
The models of stochastic processes for the prices of commodities with another class of market assets are differenced
The first sampling algorithm of sequential importance with resampling (SISR) algorithm, that is based on the smoothing of sample points of the latent states and parameters, the procedure can be used to estimate volatility in long-term models dependent on the data
The third algorithm, a learning and smoothing mechanism from the simulated particles with a backward resampling step is used for the choice of weights
Summary
The models of stochastic processes for the prices of commodities with another class of market assets are differenced. The development of methods to determine the spot prices by the prices of futures contracts is studied. Likewise, [28] a Bayesian estimation method is proposed, the Markov chain Monte Carlo (MCMC) simulation to jointly estimate unknown parameters and states in financial models are used; the stochastic behavior of prices and volatilities in the most important commodity markets is studied, that with other stock markets is compared. An estimation methodology is developed, an estimation of states and parameters in commodity price models with structures nonlinear is proposed, that analytically in time real cannot be evaluated. Predict future price behavior, analyze changes in economic series structures, determines storage capacity for raw material products, are developed. The rest of the article is organized, as follows: In Section 2, the general problem is formulated; In Section 3, stochastic models of commodity prices are defined; In Section 4, a short review of particle filtering and three smoothing algorithms are proposed; In Section 5, the results are discussed; and in Section 6, a discussion and conclusions are established
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