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Adaptive Mesh Modeling And Barrier Option Pricing Under A Jump-Diffusion Process

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  • Michael Albert
  • Jason Fink
  • Kristin E. Fink

Abstract

The computational burden of numerical barrier option pricing is significant, even prohibitive, for some parameterizations-especially for more realistic models of underlying asset behavior, such as jump diffusions. We extend a binomial jump diffusion pricing algorithm into a trinomial setting and demonstrate how an adaptive mesh may fit into the model. Our result is a barrier option pricing method that employs fewer computational resources, reducing run times substantially. We demonstrate that this extension allows the pricing of options that were previously computationally infeasible and examine the parameterizations in which use of the adaptive mesh is most beneficial. (c) 2008 The Southern Finance Association and the Southwestern Finance Association.

Suggested Citation

  • Michael Albert & Jason Fink & Kristin E. Fink, 2008. "Adaptive Mesh Modeling And Barrier Option Pricing Under A Jump-Diffusion Process," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 31(4), pages 381-408.
  • Handle: RePEc:bla:jfnres:v:31:y:2008:i:4:p:381-408
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    5. Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    6. Broadie, Mark & Kaya, Özgür, 2007. "A Binomial Lattice Method for Pricing Corporate Debt and Modeling Chapter 11 Proceedings," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(02), pages 279-312, June.
    7. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    8. D. Andricopoulos, Ari & Widdicks, Martin & Newton, David P. & Duck, Peter W., 2007. "Extending quadrature methods to value multi-asset and complex path dependent options," Journal of Financial Economics, Elsevier, vol. 83(2), pages 471-499, February.
    9. Hilliard, Jimmy E. & Schwartz, Adam, 2005. "Pricing European and American Derivatives under a Jump-Diffusion Process: A Bivariate Tree Approach," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(03), pages 671-691, September.
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