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Lattice Option Pricing By Multidimensional Interpolation

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  • Vladislav Kargin

Abstract

This paper 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, which 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.

Suggested Citation

  • Vladislav Kargin, 2005. "Lattice Option Pricing By Multidimensional Interpolation," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 635-647, October.
    • Handle: RePEc:bla:mathfi:v:15:y:2005:i:4:p:635-647
    DOI: 10.1111/j.1467-9965.2005.00254.x
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    1. repec:hum:wpaper:sfb649dp2006-051 is not listed on IDEAS
    2. David A. Goldberg & Yilun Chen, 2018. "Polynomial time algorithm for optimal stopping with fixed accuracy," Papers 1807.02227, arXiv.org, revised May 2024.
    3. Anne Laure Bronstein & Gilles Pagès & Jacques Portès, 2013. "Multi-asset American Options and Parallel Quantization," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 547-561, September.
    4. Denis Belomestny & Grigori Milstein & Vladimir Spokoiny, 2009. "Regression methods in pricing American and Bermudan options using consumption processes," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 315-327.
    5. Ivivi J. Mwaniki, 2017. "On skewed, leptokurtic returns and pentanomial lattice option valuation via minimal entropy martingale measure," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1358894-135, January.
    6. François-Heude, Alain & Yousfi, Ouidad, 2013. "A Generalization of Gray and Whaley's Option," MPRA Paper 47908, University Library of Munich, Germany, revised 30 Jun 2013.

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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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