Pricing of Compound Exchange Options

Abstract

In this paper we derive the pricing formula for a compound exchange option, which we refer to as ComEx option. We also run a Monte Carlo simulation to compute the intrinsic value of this option at maturity under various parameter settings, to highlight the differences and similarities between the ComEx option and the Margrabe option, which serves as a benchmark in our calculations. The ComEx option is an option, which provides the right to its owner to exchange two options, while the Margrabe option gives the right to its owner to exchange two underlying assets. The two underlying assets of the Margrabe option will be the underlying assets of the two options in the ComEx option throughout the paper. Our results show that we have successfully derived the pricing formula for the ComEx option, and we demonstrate that the price evolution of the Margrabe-, and the ComEx options are quite similar, with the main difference being in scale. In most cases, the option on exchanging the underlying assets is worth more than the option to exchange the options, as it reduces risk. We also analyze the sensitivity of the option prices at maturity to changes in correlation and volatility parameters.

Keywords: Compound options, Margrabe options, Exotic options

JEL Classification: G12, G17, G23