Option valuation with co-integrated asset prices

✍ Scribed by Jin-Chuan Duan; Stanley R. Pliska

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 403 KB
• Volume: 28
• Category: Article
• ISSN: 0165-1889
• DOI: 10.1016/s0165-1889(03)00042-3

✦ Synopsis

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-speciÿcation e ect 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, di usion limit of the asset price system and empirically studies the co-integration e ect 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.