Option Pricing for Co-Integrated Assets

Many financial data series are known to be co-integrated. The implications of this for option valuation are studied in this article. Since co-integration is commonly considered in a discrete time context, here we take a GARCH option pricing approach. In the course of doing so, we present new theoretical results for a discrete time price process to be co-integrated. Our option pricing results are consistent with economic principles: with deterministic volatilities the option prices do not depend on the co-integration parameters, except for the statistical 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. Our results for discrete time suggest there is considerable potential for further research on continuous time modeling of co-integrated price systems and on option models that are based on such continuous time processes.