On Exchange Options with Jumps

G.H.L. Cheang (Singapore), C. Chiarella, and A. Ziogas (Australia)


Financial derivatives, exchange options, compound Pois son processes, equivalent martingale measure.


Margrabe provides a pricing formula for an exchange op tion where the distributions of both stock prices are log normal with correlated Wiener components. Merton has provided a formula for the price of a European call op tion on a single stock where the stock price process con tains a continuous Poisson jump component, in addition to a continuous log-normally distributed component. We use Merton’s analysis to extend Margrabe’s results to the case of exchange options where both stock price processes also contain compound Poisson jump components. A Radon Nikod´ym derivative process that induces the change of measure from the market measure to an equivalent mar tingale measure is introduced. The choice of parameters in the Radon-Nikod´ym derivative allows us to price the option under different financial-economic scenarios.

Important Links:

Go Back