Dynamic Jump Intensities and Risk Premiums in Crude Oil Futures and Options Markets

Abstract

A tremendous amount of theoretical and empirical research has been devoted to modeling the dynamics of stock returns and applying this knowledge to valuing equity derivatives. The statistical evidence indicates that the returns process exhibits time-varying diffusive volatility and stochastic jumps in returns, and probably in volatility as well. Moreover, the parameters governing this process appear to drift over time. Yet prices for crude oil and other commodities have not been explored nearly as much, although they are volatile, crucially important to the real economy, and have actively traded futures and options. In this article, the authors go a long way toward correcting this lacuna for derivatives based on crude oil. Their approach is at the current frontier for research on equity derivatives, or indeed beyond it since they allow the jump intensity to vary stochastically over time. Their large sample of daily data spans nearly 25 years of crude oil futures and options, including multiple maturities and degrees of moneyness on each date. Bringing information from both the futures and options markets into the estimation allows much greater statistical power and, more importantly, enforces consistency in the modeling of both derivatives and their underlying. This is a significant advance in our understanding of the price dynamics of the most important commodity, and the futures and option contracts that are based on it.