Leverage Effect and Stochastic Volatility in the Agricultural Commodity Market under the CEV Model

Abstract

The problem of price fluctuation is crucial to the concept of financial engineering nowadays. The aim of this paper is twofold; first to investigate the leverage effect of the main agricultural commodities – wheat and corn, i. e. the relationship between monetary returns and the volatility of commodity prices and, secondly to capture their stochastic volatility by forming an appropriate model. The data are considered as ‘post‑crisis’ data. That means the period after the biggest shock to the world economy. Thus, the Constant Elasticity of Variance (CEV) model is used calibrated to the Generalized Method of Moments (GMM). The paper is briefly based on the research of Geman and Shih (2009), who propose an extension in capturing the leverege effect in the commodity market. Their results show a positive relationship between commodity price returns and the volatility in both the corn and wheat derivative market. According to these results, corn futures prices are characterized significantly under the CEV model. On the other side in the wheat futures market exists a driftless condition by using stochastic volatility models.