Zhylyevskyy, Oleksandr

Theoretical Economics Letters Vol. 2 no. 4 (October 2012): 400-407.

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.

Keywords: stochastic volatility, Bates model, jump-diffusion, characteristic function, option pricing