Pricing Options under Generalized GARCH and Stochastic Volatility Processes


  • The authors gratefully acknowledge support from the Australian Research Council, Macquarie Investment Management Limited, and Axiom Funds Management Corporation under Collaborative Research Grant C595301128. We have benefited from the comments of René Stulz, the referee, Jin-Chuan Duan, Ivilina Popova, L. Sankarasubra-manian, and participants at the 4th Annual CAP Workshop on Mathematical Finance at Columbia University, the 7th Annual Derivatives Securities Conference at Queen's University, the 10th Annual Australian Finance and Banking Conference, the 1997 Quantitative Methods in Finance Conference in Australia, the 1997 INFORMS in Dallas, the 1998 American Finance Association Meetings in Chicago, and at seminars at Macquarie Bank, Macquarie University, Princeton University, the University of Auckland, the University of New South Wales, and the University of Western Australia.


In this paper, we develop an efficient lattice algorithm to price European and American options under discrete time GARCH processes. We show that this algorithm is easily extended to price options under generalized GARCH processes, with many of the existing stochastic volatility bivariate diffusion models appearing as limiting cases. We establish one unifying algorithm that can price options under almost all existing GARCH specifications as well as under a large family of bivariate diffusions in which volatility follows its own, perhaps correlated, process.