Contingent Claims on Foreign Assets Following Jump-Diffusion Processes

Abstract

In this paper we price contingent claims on several foreign assetsthat follow jump-diffusion processes. Discontinuities (jumps) arise dueto the assets' movement in the respective countries, or the exchangerates, or both. We assume the existence of multiple classes (sources)of jumps. Each jump can affect one or more state-variables and is definedby its intensity of arrival and by the joint probability distributionof its magnitude. The existence of jumps gives rise to significant deviationsfrom the joint lognormality assumptions of the multivariate geometricBrownian motion, and affords more flexibility in capturing the empiricallyobserved asymmetry and fat tails in asset returns. Analytic solutionsare provided for the European option on the best of several assets withoutor with exchange rate (quanto-type) protection. A Markov-chainnumerical method that can also handle American claims is given and itsaccuracy is demonstrated. Neglecting the effect of jumps causes seriousmisspricing and leads to erroneous decision-making when purchasing orexercising such options.