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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 17140.

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Date of creation: 06 Sep 2009
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Handle: RePEc:pra:mprapa:17140

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Keywords: Option Pricing; Nonparametric; Entropy;

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References

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  1. Guido W Imbens, Phillip Johnson & Richard H Spady, . "Information theoretic approaches to inference in moment condition model," Economics Papers W12., Economics Group, Nuffield College, University of Oxford.
  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. Robertson, John C & Tallman, Ellis W & Whiteman, Charles H, 2005. "Forecasting Using Relative Entropy," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 37(3), pages 383-401, June.
  4. Mark Broadie & Jérôme B. Detemple & Eric Ghysels & Olivier Torrès, 1996. "American Options with Stochastic Dividends and Volatility: A Nonparametric Investigation," CIRANO Working Papers 96s-26, CIRANO.
  5. Walker, Todd & Haley, M. Ryan & McGee, M. Kevin, 2009. "Disparity, Shortfall, and Twice-Endogenous HARA Utility," MPRA Paper 17139, University Library of Munich, Germany.
  6. Bera, Anil K. & Bilias, Yannis, 2002. "The MM, ME, ML, EL, EF and GMM approaches to estimation: a synthesis," Journal of Econometrics, Elsevier, Elsevier, vol. 107(1-2), pages 51-86, March.
  7. René Garcia & Ramazan Gençay, 1998. "Pricing and Hedging Derivative Securities with Neural Networks and a Homogeneity Hint," CIRANO Working Papers 98s-35, CIRANO.
  8. Imbens, G.W. & Johnson, P. & Spady, R.H., 1995. "Information Theoretic Approaches to Inference in Movement Condition Models," Economics Papers 99, Economics Group, Nuffield College, University of Oxford.
  9. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, Econometric Society, vol. 65(4), pages 861-874, July.
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Cited by:
  1. 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, Elsevier, vol. 18(2), pages 341-352, March.

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