Pricing of basket options using dimension reduction and adaptive finite differences in space, and discontinuous galerkin in time

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Abstract

European basket options are priced by solving the multi-dimensional Black–Scholes–Merton equation. Standard numerical methods to solve these problems often suffer from the “curse of dimensionality”. We tackle this by using a dimension reduction technique based on a principal component analysis with an asymptotic expansion. Adaptive finite differences are used for the spatial discretization. In time we employ a discontinuous Galerkin scheme. The efficiency of our proposed method to solve a five-dimensional problem is demonstrated through numerical experiments and compared with a Monte-Carlo method.

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von Sydow, L., Ghafari, P., Lehto, E., & Wångersjö, M. (2016). Pricing of basket options using dimension reduction and adaptive finite differences in space, and discontinuous galerkin in time. In Lecture Notes in Computational Science and Engineering (Vol. 112, pp. 607–615). Springer Verlag. https://doi.org/10.1007/978-3-319-39929-4_58

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