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Parametric properties of semi-nonparametric distributions, with applications to option valuation

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Author Info
Ángel León () (Universidad de Alicante)
Javier Mencía () (Banco de España)
Enrique Sentana () (Centro de Estudios Monetarios y Financieros (CEMFI))

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Abstract

We derive the statistical properties of the SNP densities of Gallant and Nychka (1987). We show that these densities, which are always positive, are more flexible than truncated Gram-Charlier expansions with positivity restrictions. We use the SNP densities for financial derivatives valuation. We relate real and risk-neutral measures, obtain closed-form prices for European options, and analyse the semiparametric properties of our pricing model. In an empirical application to S&P500 index options, we compare our model to the standard and Practitioner's Black-Scholes formulas, truncated expansions, and the Generalised Beta and Variance Gamma models.

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File URL: http://www.bde.es/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/07/Fic/dt0707e.pdf
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File Function: First version, March 2007
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Paper provided by Banco de España in its series Banco de España Working Papers with number 0707.

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Length: 60 pages
Date of creation: Mar 2007
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Handle: RePEc:bde:wpaper:0707

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Related research
Keywords: kurtosis; density expansions; gram-charlier; skewness; s&p index options;

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Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions

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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. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January. [Downloadable!] (restricted)
  2. Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Skewness and Kurtosis Implied by Option Prices: A Second Comment," FMG Discussion Papers dp419, Financial Markets Group. [Downloadable!] (restricted)
  3. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October. [Downloadable!] (restricted)
  4. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179. [Downloadable!] (restricted)
  5. C. J. Corrado, Tie Su, 1997. "Implied volatility skews and stock return skewness and kurtosis implied by stock option prices," European Journal of Finance, Taylor and Francis Journals, vol. 3(1), pages 73-85, March. [Downloadable!] (restricted)
  6. Victor Fenton & Gallant, A. Ronald, 1996. "Qualitative and Asymptotic Performance of SNP Density Estimators," Working Papers 96-17, Duke University, Department of Economics.
  7. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November. [Downloadable!] (restricted)
  8. Henri Bertholon ; Alain Monfort ; Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Centre de Recherche en Economie et Statistique, revised 2006. [Downloadable!]
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  9. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March. [Downloadable!] (restricted)
  10. V. L. Martin & G. M. Martin & G. C. Lim, 2005. "Parametric pricing of higher order moments in S&P500 options," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 377-404. [Downloadable!]
    Other versions:
  11. Corrado, Charles J & Su, Tie, 1996. "Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices," Journal of Financial Research, Southern Finance Association and Southwestern Finance Association, vol. 19(2), pages 175-92, Summer.
  12. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  13. Capelle-Blancard, Gunther & Jurczenko, Emmanuel & Maillet, Bertrand, 2001. "The approximate option pricing model: performances and dynamic properties," Journal of Multinational Financial Management, Elsevier, vol. 11(4-5), pages 427-443, December. [Downloadable!] (restricted)
  14. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October. [Downloadable!] (restricted)
  15. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  16. Fenton, Victor M. & Gallant, A. Ronald, 1996. "Qualitative and asymptotic performance of SNP density estimators," Journal of Econometrics, Elsevier, vol. 74(1), pages 77-118, September. [Downloadable!] (restricted)
  17. 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 637-54, May-June. [Downloadable!] (restricted)
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