Option Valuation with Co-Integrated Asset Prices

Posted: 27 Dec 2000

See all articles by Jin-Chuan Duan

Jin-Chuan Duan

National University of Singapore (NUS) - Business School and Risk Management Institute

Stanley R. Pliska

University of Illinois at Chicago - Department of Finance

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 better understand these results, 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.

Suggested Citation

Duan, Jin-Chuan and Pliska, Stanley R., Option Valuation with Co-Integrated Asset Prices. Journal of Economic Dynamics and Control, Vol. 28, No. 4, pp. 727-754, 2004, Available at SSRN: https://ssrn.com/abstract=243393 or http://dx.doi.org/10.2139/ssrn.243393

Jin-Chuan Duan (Contact Author)

National University of Singapore (NUS) - Business School and Risk Management Institute ( email )

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Singapore, 117592
Singapore

Stanley R. Pliska

University of Illinois at Chicago - Department of Finance ( email )

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Chicago, IL 60607-7124
United States
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