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A New Spectral Element Method for Pricing European Options Under the Black–Scholes and Merton Jump Diffusion Models

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Abstract

We present a new spectral element method for solving partial integro-differential equations for pricing European options under the Black–Scholes and Merton jump diffusion models. Our main contributions are: (i) using an optimal set of orthogonal polynomial bases to yield banded linear systems and to achieve spectral accuracy; (ii) using Laguerre functions for the approximations on the semi-infinite domain, to avoid the domain truncation; and (iii) deriving a rigorous proof of stability for the time discretizations of European put options under both the Black–Scholes model and the Merton jump diffusion model. The new method is flexible for handling different boundary conditions and non-smooth initial conditions for various contingent claims. Numerical examples are presented to demonstrate the efficiency and accuracy of the new method.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907-1957, USA

    Feng Chen & Jie Shen

  2. LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Haijun Yu

Authors
  1. Feng Chen
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  2. Jie Shen
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  3. Haijun Yu
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Correspondence to Jie Shen.

Additional information

This work is partially supported by NSF DMS-0915066 and AFOSR FA9550-08-1-0416.

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Chen, F., Shen, J. & Yu, H. A New Spectral Element Method for Pricing European Options Under the Black–Scholes and Merton Jump Diffusion Models. J Sci Comput 52, 499–518 (2012). https://doi.org/10.1007/s10915-011-9556-5

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  • DOI: https://doi.org/10.1007/s10915-011-9556-5

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