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

Christophe de Luigi 1 Jérôme Lelong 2 Sylvain Maire 1, 3
2 DAO - Données, Apprentissage et Optimisation
LJK - Laboratoire Jean Kuntzmann
3 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
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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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, Elsevier, 2016, 100, pp.14-30. ⟨10.1016/j.apnum.2015.11.001⟩. ⟨hal-00746872⟩

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