CLOSED FORM VALUATION OF AMERICAN BARRIER OPTIONS

Espen Gaarder Haug
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Espen Gaarder Haug: Amaranth Advisors, Two American Lane, Greenwich, CT 06836, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2001, vol. 04, issue 02, 355-359

Abstract: Closed form formulae for European barrier options are well known from the literature. This is not the case for American barrier options, for which no closed form formulae have been published. One has therefore had to resort to numerical methods. Lattice models like a binomial or a trinomial tree, for valuation of barrier options are known to converge extremely slowly, compared to plain vanilla options. Methods for improving the algorithms have been described by several authors. However, these are still numerical methods that are quite computer intensive. In this paper we show how some American barrier options can be valued analytically in a very simple way. This speeds up the valuation dramatically as well as give new insight into barrier option valuation.

Keywords: American barrier options; geometric Brownian motion; reflection principle; closed form solutions (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0219024901001012

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