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Journal Articles Applied Numerical Mathematics Year : 2016

Robust adaptive numerical integration of irregular functions with applications to basket and other multi-dimensional exotic options

Abstract

We improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting strategy based on a geometrical criterion. This algorithm is tested especially on the pricing of multidimensional vanilla options in the Black–Scholes framework which emphasizes the numerical problems of integrating non-smooth functions. In high dimensions, this new algorithm is used as a control variate after a dimension reduction based on principal component analysis. Numerical tests are performed on the Genz package, on the pricing of basket, put on minimum and digital options in dimensions up to ten.
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Dates and versions

hal-00746872 , version 1 (29-10-2012)

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Christophe de Luigi, Jérôme Lelong, Sylvain Maire. Robust adaptive numerical integration of irregular functions with applications to basket and other multi-dimensional exotic options. Applied Numerical Mathematics, 2016, 100, pp.14-30. ⟨10.1016/j.apnum.2015.11.001⟩. ⟨hal-00746872⟩
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