Pricing Multi-Asset Options with an External Barrier

Yue-Kuen Kwok (), Lixin Wu and Hong Yu
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Yue-Kuen Kwok: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
Lixin Wu: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
Hong Yu: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China

International Journal of Theoretical and Applied Finance (IJTAF), 1998, vol. 01, issue 04, 523-541

Abstract: An external barrier of an option contract is a stochastic variable which determines whether the option is knocked in or out when the value of the variable is above or below some predetermined level, but itself is not the price of an asset which underlies the option. In this paper, we present analytic formulation for the valuation of European options on one or multiple assets with single external barrier, where the barrier level can be exponential. As the domain of the problem becomes semi-infinite due to the presence of the external barrier, we employ the method of images to find the Green function of the governing differential equation. An efficient and accurate fractional step finite difference scheme is proposed for the numerical valuation of these barrier options.

Keywords: Multi-asset options; external barrier; Green's function; fractional step finite difference schemes; JEL classification code: G130 (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1142/S021902499800028X

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