A Stochastic-Volatility Model for Pricing Power Variants of Exchange Options

Abstract

In this article, we present a model with jumps and stochastic volatility, based on two correlated variance-gamma processes combined with an Ornstein-Uhlenbeck process with gamma innovations. Our objective is to analyze pricing methods for a European-style equity option to exchange one stock for another, as well as two important classes of its variants that raise the stock prices and the standard option payoff, respectively, to certain powers. These option variants are particularly useful in adjusting the risk level of exchange options and can also be viewed as generalizations of traditional power-type options. The pricing formulas are obtained under risk neutrality in terms of characteristic functions and are thus independent from the model distribution. Numerical results are given for illustrating the efficiency of the presented formulas along with various advantages of the proposed stochastic-volatility model.

TOPICS: Options, statistical methods, performance measurement