Particle Filter-based Empirical Studies Of Commodity Prices

In this article,we firstly describe and compare two two-factor models of the stochastic behavior of commodity Price,in terms of their ability to price existing futures contracts.The first two-factor model developed by Gibson and Schwartz (1990) first.It assumes that the commodity spot price follows the Geometric Brownian Motion,the convenience yield follows Ornstein-Uhlenbeck (O-U)process which has a mean reverting character.The second two-factor model extends the first two-factor model by adding two new features. First,the Ornstein-Uhlenbeck process for the convenience yield is replaced by a Cox-Ingersoll-Ross(CIR) pro-cess.This ensures that our model is arbitrage-free.Secord,spot price volatility is proportional to the square root of the convenience yield level.Then we present the Extended Kalman Filter and Particle Filter methodlogy.By rewrite the sec-ond two-factor model we obtain measure equation and transformation equation. Finally,by using Particle Filter methodlogy,we estimate the parameters of the two-factor model for one commercial of copper and present the statistic explana-tions of the parameters.