American-type basket option pricing: a simple two-dimensional partial differential equation

Hamza Hanbali and Daniel Linders

Quantitative Finance, 2019, vol. 19, issue 10, 1689-1704

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.

Date: 2019
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DOI: 10.1080/14697688.2019.1588987

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