Joint Characteristic Function of Stock Log-Price and Squared Volatility in the Bates Model and Its Asset Pricing Applications

Oleksandr Zhylyevskyy

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

DOI: 10.4236/tel.[phone]                

Abstract

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

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

Conflicts of Interest

The authors declare no conflicts of interest.

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