An Efficient Algorithm for Options Under Merton’s Jump-Diffusion Model on Nonuniform Grids

An Efficient Algorithm for Options Under Merton’s Jump-Diffusion Model on Nonuniform Grids 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 · http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Economics Springer Journals

An Efficient Algorithm for Options Under Merton’s Jump-Diffusion Model on Nonuniform Grids

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Economics; Economic Theory/Quantitative Economics/Mathematical Methods; Computer Appl. in Social and Behavioral Sciences; Operations Research/Decision Theory; Behavioral/Experimental Economics; Math Applications in Computer Science
ISSN
0927-7099
eISSN
1572-9974
D.O.I.
10.1007/s10614-018-9823-8
Publisher site
See Article on Publisher Site

Abstract

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 ·

Journal

Computational EconomicsSpringer Journals

Published: Jun 2, 2018

References

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