Subordinated Levy Processes and Applications to Crude Oil Options

Abstract

One approach to oil markets is to treat oil as an asset, besides its role as a commodity. Speculative and nonspeculative activity by investors in the derivatives markets could be responsible for a sizable increase in oil prices. This paper recognizes both the consumption and investment aspects of crude oil and proposes Levy processes for modeling uncertainty and options pricing. Calibration to crude oil futures` options shows high volatility of oil futures prices, fat-tailed, and right-skewed market expectations,implying a higher probability mass on crude oil prices remaining above the futures` level. These findings support the view that demand for futures contracts by investors could lead to excessively high price volatility.

Keywords: Characteristic functions, Esscher transform, Fourier transform, Inverse problem, Levy processes, Option pricing, Risk-neutral density, Volatility

JEL Classification: C63, G13, Q49