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Alternative Tilts for Nonparametric Option Pricing

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  • Walker, Todd B
  • Haley, M. Ryan

Abstract

This paper generalizes the nonparametric approach to option pricing of Stutzer (1996) by demonstrating that the canonical valuation methodology in- troduced therein is one member of the Cressie-Read family of divergence mea- sures. While the limiting distribution of the alternative measures is identical to the canonical measure, the finite sample properties are quite different. We assess the ability of the alternative divergence measures to price European call options by approximating the risk-neutral, equivalent martingale measure from an empirical distribution of the underlying asset. A simulation study of the finite sample properties of the alternative measure changes reveals that the optimal divergence measure depends upon how accurately the empirical distri- bution of the underlying asset is estimated. In a simple Black-Scholes model, the optimal measure change is contingent upon the number of outliers observed, whereas the optimal measure change is a function of time to expiration in the stochastic volatility model of Heston (1993). Our extension of Stutzer’s tech- nique preserves the clean analytic structure of imposing moment restrictions to price options, yet demonstrates that the nonparametric approach is even more general in pricing options than originally believed.

Suggested Citation

  • Walker, Todd B & Haley, M. Ryan, 2009. "Alternative Tilts for Nonparametric Option Pricing," MPRA Paper 17140, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:17140
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    File URL: https://mpra.ub.uni-muenchen.de/17140/1/MPRA_paper_17140.pdf
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    References listed on IDEAS

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    1. Robertson, John C & Tallman, Ellis W & Whiteman, Charles H, 2005. "Forecasting Using Relative Entropy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 383-401, June.
    2. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 143-159, March.
    3. Bera, Anil K. & Bilias, Yannis, 2002. "The MM, ME, ML, EL, EF and GMM approaches to estimation: a synthesis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 51-86, March.
    4. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    5. Garcia, Rene & Gencay, Ramazan, 2000. "Pricing and hedging derivative securities with neural networks and a homogeneity hint," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 93-115.
    6. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "American options with stochastic dividends and volatility: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 53-92.
    7. M. Ryan Haley & M. Kevin McGee & Todd B. Walker, 2013. "Disparity, Shortfall, and Twice-Endogenous HARA Utility," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 524-541, December.
    8. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
    9. Jamie Alcock & Trent Carmichael, 2008. "Nonparametric American option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(8), pages 717-748, August.
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    Cited by:

    1. Smith, Godfrey, 2013. "Simulated testing of nonparametric measure changes for hedging European options," Finance Research Letters, Elsevier, vol. 10(2), pages 93-101.
    2. Haley, M. Ryan & McGee, M. Kevin, 2011. ""KLICing" there and back again: Portfolio selection using the empirical likelihood divergence and Hellinger distance," Journal of Empirical Finance, Elsevier, vol. 18(2), pages 341-352, March.

    More about this item

    Keywords

    Option Pricing; Nonparametric; Entropy;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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