Option valuation with co-integrated asset prices

Abstract

This paper investigates theoretical and practical aspects of options that are based upon two or more assets which are co-integrated. For this purpose, a new, discrete-time model of asset prices is developed, a model featuring both the co-integration property as well as stochastic volatilities. Using a GARCH, equilibrium-based option pricing approach, it is shown that when volatilities are deterministic the option prices do not depend on the co-integration parameters, except for the mis-specification effect as to the manner in which the volatilities are estimated. However, with stochastic volatilities the option prices explicitly depend upon the co-integration parameters. In order to understand these results better, this paper also examines a continuous-time, diffusion limit of the asset price system and empirically studies the co-integration effect using spread options based upon the S&P500 and the NASDAQ100. These numerical results suggest that consideration of co-integration can substantially alter the value, delta and vega of a spread option.