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An efficient and accurate lattice for pricing derivatives under a jump-diffusion process

Published: 08 March 2009 Publication History

Abstract

Derivatives are popular financial instruments that play essential roles in financial markets. However, most derivatives have no analytical formulas and must be priced by numerical methods such as lattice models. The pricing results generated by a lattice converge to the theoretical values, but they may converge slowly or even oscillate significantly due to the nonlinearity error. According to empirical studies, a lognormal diffusion process, which has been widely studied, does not capture the real world phenomena well. To address these problems, this paper proposes a novel lattice under the jump-diffusion processes. Our lattice is accurate because it suppresses the nonlinearity error. It is more efficient due to the fact that the time complexity of our lattice is lesser than those of the other existing lattice models. Numerous numerical calculations confirm the superior performance of our lattice model to the other existing methods.

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J. E. Hilliard and A. Schwartz. Pricing European and American Derivatives Under a Jump-Diffusion Process: A Bivariate Tree Approach. J. Finan. Quant. Anal., 40(3): 671--691, 2005.
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Y.-D. Lyuu. Financial Engineering and Computation: Principles, Mathematics, Algorithms. Cambridge University Press, 2002.
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cover image ACM Conferences
SAC '09: Proceedings of the 2009 ACM symposium on Applied Computing
March 2009
2347 pages
ISBN:9781605581668
DOI:10.1145/1529282
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 March 2009

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Author Tags

  1. complexity
  2. jump-diffusion process
  3. pricing algorithm

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SAC09
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SAC09: The 2009 ACM Symposium on Applied Computing
March 8, 2009 - March 12, 2008
Hawaii, Honolulu

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Overall Acceptance Rate 1,650 of 6,669 submissions, 25%

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