The option on n assets with exchange rate and exercise price risk

Abstract

Solutions to the call option on the maximum or the minimum of n assets are explicitly provided when the exercise price is stochastic, and all assets carry both asset price and exchange rate risk in a n+1 country model with 2( n+1) state variables. The model can be seen as an extension of Johnson (Johnson, H., 1987. Options on the maximum or the minimum of several assets. Journal of Financial and Quantitative Analysis 22, 227–283), Margrabe (Margrabe, W., 1978. The value of an option to exchange one asset for another. Journal of Finance 33, 177–186), and Reiner (Reiner, E., 1992. Quanto mechanics, RISK, March, 59–63), and it is useful for valuation of both financial and real options. As an application, a contract is valued that allows a portfolio manager to participate in the out-performance of the returns of international assets, portfolios or stock indexes.