Jumps and Stochastic Volatility in Crude Oil Prices and Advances in Average Option Pricing

Abstract

Crude oil derivatives form an important part of the global derivatives market. In this paper, we focus on Asian options which are favoured by risk managers being effective and cost-saving hedging instruments. The paper has both empirical and theoretical contributions: we conduct an empirical analysis of the crude oil price dynamics and develop an accurate pricing setup for arithmetic Asian options with discrete and continuous monitoring featuring stochastic volatility and discontinuous underlying asset price movements. Our theoretical contribution is applicable to various commodities exhibiting similar stylized properties. We here estimate the stochastic volatility model with price jumps as well as the nested model with omitted jumps to NYMEX WTI futures vanilla options. We find that price jumps and stochastic volatility are necessary to fit options. Despite the averaging effect, we show that Asian options remain sensitive to jump risk and that ignoring the discontinuities can lead to substantial mispricings.

Keywords: Oil prices, stochastic volatility, jump diffusion, arithmetic Asian options

JEL Classification: G12, G13, C63, C13