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Lattice Option Pricing By Multidimensional Interpolation

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Author Info
Vladislav Kargin (Cornerstone Research)

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Abstract

This note proposes a method for pricing high-dimensional American options based on modern methods of multidimensional interpolation. The method allows using sparse grids and thus mitigates the curse of dimensionality. A framework of the pricing algorithm and the corresponding interpolation methods are discussed, and a theorem is demonstrated that suggests that the pricing method is less vulnerable to the curse of dimensionality. The method is illustrated by an application to rainbow options and compared to Least Squares Monte Carlo and other benchmarks.

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File URL: http://129.3.20.41/eps/fin/papers/0309/0309003.pdf
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Publisher Info
Paper provided by EconWPA in its series Finance with number 0309003.

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Length: 17 pages
Date of creation: 07 Sep 2003
Date of revision: 29 Oct 2004
Handle: RePEc:wpa:wuwpfi:0309003

Note: Type of Document - pdf; prepared on IBM PC ; pages: 17; figures: included
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Web page: http://129.3.20.41

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Related research
Keywords: interpolation; option pricing;

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Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 14(1), pages 113-47.
  2. Boyle, Phelim P & Evnine, Jeremy & Gibbs, Stephen, 1989. "Numerical Evaluation of Multivariate Contingent Claims," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 2(2), pages 241-50. [Downloadable!] (restricted)
  3. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March. [Downloadable!]
  4. Barraquand, J?r?me & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(03), pages 383-405, September. [Downloadable!]
  5. 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. [Downloadable!] (restricted)
  6. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June. [Downloadable!] (restricted)
  7. Madan, Dilip B & Milne, Frank & Shefrin, Hersh, 1989. "The Multinomial Option Pricing Model and Its Brownian and Poisson Limits," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 2(2), pages 251-65. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Denis Belomestny & Grigori N. Milstein & Vladimir Spokoiny, 2006. "Regression methods in pricing American and Bermudan options using consumption processes," SFB 649 Discussion Papers SFB649DP2006-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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