Currency Derivatives

In this chapter we develop a theory for derivatives based on the exchange rate between two (or more) currencies. This is initially done using classical delta hedging methods, but the main part of the theory is developed using martingale methods. We discuss the foreign and the domestic martingale measures and the relations between these measures, and in particular we show that the likelihood ratio between the measures equals the ratio between the foreign and the domestic stochastic discount factors. Option pricing formulas are also derived, and we discuss the Siegel paradox.