Pricing of Asian Exchange Rate Options Under Stochastic Interest Rates As a Sum of Options

25 Pages Posted: 17 May 2006

See all articles by J. Aase Nielsen

J. Aase Nielsen

Aarhus University - Department of Theoretical Statistics and Operations Research

Klaus Sandmann

University of Bonn - The Bonn Graduate School of Economics

Abstract

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.

Keywords: Asian Exchange Rate Option, Forward Risk Adjusted Measure, Stochastic Interest Rates

JEL Classification: G13

Suggested Citation

Nielsen, Jørgen 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: https://ssrn.com/abstract=901948

Jørgen Aase Nielsen

Aarhus University - 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 )

Adenauerallee 24-26
Bonn, D-53113
Germany

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