Pricing of Asian exchange rate options under stochastic interest rates as a sum of options

The aim of the paper is to develop pricing formulas for long term 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. <p>The 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 extension of results developed by Rogers and Shi (1995) and Jamshidian (1991). In addition bounds for the pricing error are determined. Comparing with Monte Carlo simulation the pricing is found to be very precise.