Efficient numerical methods for the valuation of American barrier options

Dlamini, Mkhululi

Efficient numerical methods for the valuation of American barrier options

Thesis / Dissertation

2002

Abstract

[Thesis has an accompanying disc.] The barrier option is the most popular exotic option traded today. Because such options have a discontinuous payoff pattern, their accurate valuation is a particular challenge. Most popular in the OTC market, a lack of a liquid secondary market in these products has meant that very often, an early exercise feature is added to the contract. This makes it of particular interest to study efficient numerical methods for the valuation of American barrier options . This thesis considers three methods that have been developed to price such options; the Ritchken Trinomial Method <RTM), the Finite Difference Method <FDM> and the Finite Element Method <FEM>. First an account is given of the barrier option pricing problem accompanied by a description of the behavior of barrier option price and delta curves. Then the theory and implementation of each method is described in turn. Finally a detailed computational analysis is given where the three methods are compared in pricing and hedging applications, with concluding remarks on the performance results.

Keywords

Mathematics and Applied Mathematics

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