In this paper, we introduce a class of Lévy processes, with both a diffusion part and a pure jump component as well, as a prior distribution for log prices or of volatilities in our stochastic volatility models. We consider changes of probability measure to achieve risk-neutrality, and thus price and hedge options.

We extend the work of Duffie, Pan and Singleton (2000) to much more general processes. These authors model the jump part of the Lévy process as a compound Poisson, while we use a completely general Lévy process, and also allow dependent jumps in both (log) prices and in volatility. We show how to do option pricing using the change of measure required of us by The First Fundamental Theorem of Asset pricing (see Delbaen and Schachermayer, 1994). We will present other models in the literature as particular cases of our model. In addition, we outline a method for hedging European call options on assets driven by infinitely divisible vector processes.

Cite as:

@TechReport{terh:wolp:malo:2004,
      Author = "ter Horst, Enrique A. and Robert L. Wolpert and
                  Samuel W. Malone",
       Title = "Pricing \& Hedging Options on Assets driven by Infinitely
                  Divisible Vector Processes",
 Institution = "Duke University ISDS",
        Type = "Discussion Paper",
      Number = "04-18",
         URL = "http://ftp.stat.duke.edu/pub/WorkingPapers/04-18.html",
        Year = 2004,
}

The manuscript is available in PostScript (337 kb) and PDF (147 kb) formats.