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

Oleksandr Zhylyevskyy ()

Staff General Research Papers Archive from Iowa State University, Department of Economics

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: stochastic volatility; Bates model; jump-diffusion; characteristic function; option pricing (search for similar items in EconPapers)
Date: 2012-10-31
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Published in Theoretical Economics Letters, October 2012, vol. 2 no. 4, pp. 400-407

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http://dx.doi.org/10.4236/tel.2012.24074

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