A Jump Diffusion Model for Agricultural Commodities with Bayesian Analysis

Abstract

respectively. The financial support from Agricultural Experiment Station at South Dakota State University (Project H363-10) and Stahly Scholar in Financial Economics are gratefully acknowledged by Wang. We appreciate the comments by Wade Brorsen and Philip Garcia and other participants at the NCCC-134 conference. A Jump Diffusion Model for Agricultural Commodities with Bayesian Analysis Stochastic volatility, price jumps, seasonality, and stochastic cost of carry, have been included separately, but not collectively, in pricing models of agricultural commodity futures and options. We propose a comprehensive model that incorporates all four features. We employ a special Markov Chain Monte Carlo algorithm, new in the agricultural commodity derivatives pricing literature, to estimate the proposed stochastic volatility (SV) and stochastic volatility with jumps (SVJ) models. Overall model fitness tests favor the SVJ model. The in-sample and out-of-sample pricing and hedging results for corn, soybeans and wheat generally, with few exceptions, lend support for the SVJ model.

Time-variations in commodity price jumps

“…Obviously, fair transaction prices are important to obtain economically meaningful parameter estimates. Second, the heating oil, natural gas, corn and soybeans futures markets display important seasonal patterns at the intrayear level (Karali et al, 2011;Schmitz et al, 2014). These seasonal fluctuations are important because they are likely to introduce time-variations in the probability of jumps, which we analyze in this paper.…”

“…Hilliard & Reis (1998) and Karali et al (2011) estimate jump-diffusion models, originally developed for equity prices, in commodity markets. Sørensen (2002), Back et al (2013), Brooks & Prokopczuk (2013 and Schmitz et al (2014) propose a variety of models that capture seasonal variations in commodity returns and volatility. But none of these studies considers the time-varying probability of jumps.…”

A new technique to estimate the risk-neutral processes in jump–diffusion commodity futures models

“…Later, Miltersen and Schwartz [16] also considered a three-factor model in order to price commodity futures and futures options. More recently, in the literature, jump-diffusion models have been considered because there are numerous empirical studies which show that commodity prices exhibit jumps, [6], [21] and so on. Hilliard and Reis [12] considered a three-factor model where the spot price follows a jump-diffusion stochastic process.…”

The Jump Size Distribution of the Commodity Spot Price and Its Effect on Futures and Option Prices

“…Although this assumption is very attractive because of its computational, convenience, theoretical derivation and statistical properties, [1][2][3][4] others found significant evidence of the presence of jumps in commodity prices.…”