Empirical Hedging Performance on Long-Dated Crude Oil Derivatives

Abstract

This paper presents an empirical study on hedging long-dated crude oil futures options with forward price models incorporating stochastic interest rates and stochastic volatility. Several hedging schemes are considered including delta, gamma, vega and interest rate hedge. Factor hedging is applied to the proposed multi-dimensional models and the corresponding hedge ratios are estimated by using historical crude oil futures prices, crude oil option prices and Treasury yields. Hedge ratios from stochastic interest rate models consistently improve hedging performance over hedge ratios from deterministic interest rate models, an improvement that becomes more pronounced over periods with high interest rate volatility, such as during the GFC. An interest rate hedge consistently improves hedging beyond delta, gamma and vega hedging, especially when shorter maturity contracts are used to roll the hedge forward. Furthermore, when the market experiences high interest rate volatility and the hedge is subject to high basis risk, adding interest rate hedge to delta hedge provides an improvement, while adding gamma and/or vega to the delta hedge worsens performance.

Keywords: Stochastic interest rates, Delta hedge, Interest rate hedge, Long-dated crude oil options

JEL Classification: C13, C60, G13, Q40