European Exchange Option Pricing in Exponential Lévy Model

In this article we apply two methods to price the exchange options in exponential Levy model, where the jump parts of two driving processes are assumed to have mapping relations. One method is pricing under the minimal entropy martingale measure(MEMM) of 2-dimensional market, and the other one is Margrabe's method which has been examined to be correct for Black-Scholes model. We compare the results of two methods and find that Margrabe's method is incorrect for exponential Levy model with jumps except special states of the model.