American-type basket option pricing: a simple two-dimensional partial differential equation |
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Authors: | Hamza Hanbali Daniel Linders |
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Affiliation: | 1. Department of Accountancy, Finance and Insurance, KU, Naamsestraat 69, Leuven 3000, Belgiumhamza.hanbali@kuleuven.be;3. Department of Mathematics, University of Illinois, Urbana, IL, USA |
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Abstract: | We consider the pricing of American-type basket derivatives by numerically solving a partial differential equation (PDE). The curse of dimensionality inherent in basket derivative pricing is circumvented by using the theory of comonotonicity. We start with deriving a PDE for the European-type comonotonic basket derivative price, together with a unique self-financing hedging strategy. We show how to use the results for the comonotonic market to approximate American-type basket derivative prices for a basket with correlated stocks. Our methodology generates American basket option prices which are in line with the prices obtained via the standard Least-Square Monte-Carlo approach. Moreover, the numerical tests illustrate the performance of the proposed method in terms of computation time, and highlight some deficiencies of the standard LSM method. |
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Keywords: | Black & Scholes Basket options Pricing and hedging Comonotonicity Partial differential equations Finite difference method Least-Squares Monte-Carlo |
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