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.
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 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.
Nielsen, J. Aase and Sandmann, Klaus, Pricing of Asian Exchange Rate Options under Stochastic Interest Rates
as a Sum of Options. Finance and Stochastics, Vol. 3, No. 6, pp. 355-370, 2002. Available at SSRN: http://ssrn.com/abstract=901948
Jørgen Aase Nielsen
University of Aarhus - Department of Theoretical Statistics and Operations Research ( email )
DK-8000 Aarhus C Denmark
Klaus Sandmann (Contact Author)
University of Bonn - The Bonn Graduate School of Economics ( email )