A Systematic Approach to Pricing and Hedging of International Derivatives with Interest-Rate Risk

The paper deals with the valuation and hedging of non path- dependent European options on one or several underlyings in a model of an international economy which allows for both interest rate and exchange rate risk. The contingent claims may pay off in arbitrary currencies. Using martingale theory we provide a unified and easily applicable approach to pricing and hedging Black-Scholes type options on stocks, bonds, forwards, futures, exchange rates and indices. We also cover the pricing and hedging of options to exchange two Black-Scholes type options for one another. This class of payoffs includes for instance spread options. We give near explicit solutions for pricing and hedging of these contracts and discuss several numerical techniques for the evaluation of our formulas. In particular, using the theory of large deviation, we are able to give sharp estimates for the quality of Monte Carlo simulations