Author(s)

Oleksandr Zhylyevskyy

Department of Economics, Iowa State University, Ames, USA.

The model of Bates specifies a rich, flexible structure of stock dynamics suitable for applications in finance and economics, including valuation of derivative securities. This paper analytically derives a closed-form expression for the joint conditional characteristic function of a stock’s log-price and squared volatility under the model dynamics. The use of the function, based on inverting it, is illustrated on examples of pricing European-, Bermudan-, and American-style options. The discussed approach for European-style derivatives improves on the option formula of Bates. The suggested approach for American-style derivatives, based on a compound-option technique, offers an alternative solution to existing finite-difference methods.

Bates Model; Stochastic Volatility; Jump-Diffusion; Characteristic Function; Option Pricing

O. Zhylyevskyy, "Joint Characteristic Function of Stock Log-Price and Squared Volatility in the Bates Model and Its Asset Pricing Applications," Theoretical Economics Letters, Vol. 2 No. 4, 2012, pp. 400-407. doi: 10.4236/tel.2012.24074.