Asian Exchange Rate Options under Stochastic Interest Rates: Pricing as a Sum of Delayed Payment Options

The aim of the paper is to develop pricing formulas for European type Asian options written on the exchange rate in a two currency economy. The exchange rate as well as the foreign and domestic zero coupon bond prices are assumed to follow geometric Brownian motions. As a special case of a discrete Asian option we analyse the delayed payment currency option and develop closed form pricing and hedging formulas. The main emphasis is devoted to the discretely sampled Asian option. It is shown how the value of this option can be approximated as the sum of Black-Scholes options. The formula is obtained under the application of results developed by Rogers and Shi (1995) and Jamshidian (1991). In addition bounds for the pricing error are determined. distribution of information. This criterion allows, not only,