Joint Characteristic Function of Stock Log-Price and Squared Volatility in the Bates Model and Its Asset Pricing Applications
The model of Bates specifies a rich, flexible structure of stock dynamics suitable for applications in finance and eco- nomics, 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 exist- ing finite-difference methods
This is an article from Theoretical Economics Letters 2 (2012): 400, doi:10.4236/tel.2012.24074. Posted with permission.