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MARTINGALE APPROACH TO PRICING PERPETUAL AMERICAN OPTIONS ON TWO STOCKS

MARTINGALE APPROACH TO PRICING PERPETUAL AMERICAN OPTIONS ON TWO STOCKS We study the pricing of American options on two stocks without expiration date and with payoff functions which are positively homogeneous with respect to the two stock prices. Examples of such options are the perpetuai Margrabe option, whose payoff is the amount by which one stock outperforms the other, and the perpetual maximum option, whose payoff is the maximum of the two stock prices Our approach to pricing such options is to take advantage of their stationary nature and apply the optional sampling theorem to two martingales constructed with respect to the risk‐neutral measure the optimal exercise boundaries, which do not vary with respect to the time variable, are determined by the smooth pasting or high contact condition the martingale approach avoids the use of differential equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Finance Wiley

MARTINGALE APPROACH TO PRICING PERPETUAL AMERICAN OPTIONS ON TWO STOCKS

Mathematical Finance , Volume 6 (3) – Jul 1, 1996

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References (23)

Publisher
Wiley
Copyright
Copyright © 1996 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0960-1627
eISSN
1467-9965
DOI
10.1111/j.1467-9965.1996.tb00118.x
Publisher site
See Article on Publisher Site

Abstract

We study the pricing of American options on two stocks without expiration date and with payoff functions which are positively homogeneous with respect to the two stock prices. Examples of such options are the perpetuai Margrabe option, whose payoff is the amount by which one stock outperforms the other, and the perpetual maximum option, whose payoff is the maximum of the two stock prices Our approach to pricing such options is to take advantage of their stationary nature and apply the optional sampling theorem to two martingales constructed with respect to the risk‐neutral measure the optimal exercise boundaries, which do not vary with respect to the time variable, are determined by the smooth pasting or high contact condition the martingale approach avoids the use of differential equations.

Journal

Mathematical FinanceWiley

Published: Jul 1, 1996

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