PRICING AND HEDGING EUROPEAN OPTIONS ON FUTURES SPREADS USING THE BACHELIER SPREAD OPTION MODEL

Abstract

The Bachelier model for pricing options on futures spreads (OFS) assumes changes in the underlying .futures prices and spread follow unrestricted arithmetic Brownian motion (UABM). The assumption of UABM allows for a convenient analytic solution for the price of an OFS. The same is not possible under the more traditional assumption of geometric Brownian motion (GBM). Given the additional complexity of methods for pricing and hedging OFS using GBM such as Monte Carlo simulation and binomial trees, it is worth investigating how results from the Bachelier model compare to these other methods. The Bachelier model is presented and then extended to price an OFS with three underlying commodities. Hedge parameters for both models are provided. Results indicate that for OFS with sufficiently low volatility, differences between the Bachelier model and methods assuming GBM are quite small.