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Nonparametric Methods and Option Pricing

Author

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  • Eric Ghysels
  • Valentin Patilea
  • Éric Renault
  • Olivier Torrès

Abstract

In this paper, we survey some of the recent nonparametric estimation methods which were developed to price derivative contracts. We focus on equity options and start with a so-called model-free approach which incolves very little financial theory. Next we discuss nonparametric and semi-parametric methods of option pricing and illustrate the different approaches. Nous survolons la littérature de l'estimation non-paramétrique de modèles de titres dérivés. En particulier, nous analysons des options sur actions en partant d'une approche qui n'impose pas de restrictions théoriques, telles des restrictions d'arbitrage, et qui est donc purement statistique. Par la suite nous présentons des méthodes qui prennent avantage des restrictions a priori fournies par la théorie.

Suggested Citation

  • Eric Ghysels & Valentin Patilea & Éric Renault & Olivier Torrès, 1997. "Nonparametric Methods and Option Pricing," CIRANO Working Papers 97s-19, CIRANO.
  • Handle: RePEc:cir:cirwor:97s-19
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    References listed on IDEAS

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    1. GARCIA, René & RENAULT, Éric, 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Cahiers de recherche 9801, Universite de Montreal, Departement de sciences economiques.
    2. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, April.
    3. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    4. Hardle, W. & Vieu, P., 1990. "Kernel regression smoothing of time series," CORE Discussion Papers 1990031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    6. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
    7. Peter Bossaerts & Pierre Hillion, 1993. "A Test Of A General Equilibrium Stock Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 311-347.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Bossaerts, P. & Hafner, C. & Härdle, Wolfgang, 1996. "Foreign Exchange Rates Have Surprising Volatility," SFB 373 Discussion Papers 1996,68, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    10. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    11. Aït-Sahalia, Yacine. & Bickel, Peter J. & Stoker, Thomas M., 1994. "Goodness-of-fit tests for regression using kernel methods," Working papers 3747-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    12. repec:crs:wpaper:9329 is not listed on IDEAS
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    Cited by:

    1. Karl Härdle, Wolfgang & López-Cabrera, Brenda & Teng, Huei-Wen, 2015. "State price densities implied from weather derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 106-125.
    2. Ramazan Gencay & Aslihan Salih, 2003. "Degree of Mispricing with the Black-Scholes Model and Nonparametric Cures," Annals of Economics and Finance, Society for AEF, vol. 4(1), pages 73-101, May.
    3. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    4. Yatchew, Adonis & Hardle, Wolfgang, 2006. "Nonparametric state price density estimation using constrained least squares and the bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 579-599, August.
    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.

    More about this item

    Keywords

    Derivative securities; kernel estimation; risk neutral densities; Titres dérivés; estimation par la méthode de noyau; densités à risque neutre;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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