Comput Econ https://doi.org/10.1007/s10614-018-9823-8 An Efﬁcient Algorithm for Options Under Merton’s Jump-Diffusion Model on Nonuniform Grids 1,2 1,3 2 Yingzi Chen · Wansheng Wang · Aiguo Xiao Accepted: 24 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this paper, we consider the fast numerical valuation of European and American options under Merton’s jump-diffusion model, which is given by a partial integro-differential equations. Due to the singularities and discontinuities of the model, the time-space grids are nonuniform with reﬁnement near the strike price and expiry. On such nonuniform grids, the spatial differential operators are discretized by ﬁnite difference methods, and time stepping is performed using the discontinuous Galerkin ﬁnite element method. Owing to the nonuniform grids, algebraic multigrid method is used for solving the dense algebraical system resulting from the discretization of the integral term associated with jumps in models, which is more challenging. Numerical comparison of algebraic multigrid, the generalized minimal residual method, and the incomplete LU preconditioner shows that algebraic multigrid method is superior to and more effective than the other two methods in solving such dense algebraical system. Keywords European option pricing · American option pricing · Merton’s jump- diffusion model ·
Computational Economics – Springer Journals
Published: Jun 2, 2018
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