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

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  • Ángel León

    ()
    (Universidad de Alicante)

  • Javier Mencía

    ()
    (Banco de España)

  • Enrique Sentana

    ()
    (Centro de Estudios Monetarios y Financieros (CEMFI))

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/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/07/Fic/dt0707e.pdf
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Bibliographic Info

Paper provided by Banco de Espa�a in its series Banco de Espa�a 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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Keywords: kurtosis; density expansions; gram-charlier; skewness; s&p index options;

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  1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 51(4), pages 621-51, October.
  2. Fenton, Victor M. & Gallant, A. Ronald, 1996. "Qualitative and asymptotic performance of SNP density estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 74(1), pages 77-118, September.
  3. 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;Southwestern Finance Association, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-92, Summer.
  4. 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., John Wiley & Sons, Ltd., vol. 20(3), pages 377-404.
  5. BONTEMPS, Christian & MEDDAHI, Nour, 2002. "Testing Normality : A GMM Approach," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 2002-14, Universite de Montreal, Departement de sciences economiques.
  6. Bertholon, H. & Monfort, A. & Pegoraro, F., 2007. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working papers, Banque de France 188, Banque de France.
  7. Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Skewness and Kurtosis Implied by Option Prices: A Second Comment," FMG Discussion Papers, Financial Markets Group dp419, Financial Markets Group.
  8. Capelle-Blancard, Gunther & Jurczenko, Emmanuel & Maillet, Bertrand, 2001. "The approximate option pricing model: performances and dynamic properties," Journal of Multinational Financial Management, Elsevier, Elsevier, vol. 11(4-5), pages 427-443, December.
  9. Ronald Gallant, A. & Tauchen, George, 1999. "The relative efficiency of method of moments estimators1," Journal of Econometrics, Elsevier, Elsevier, vol. 92(1), pages 149-172, September.
  10. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  12. C. J. Corrado & Tie Su, 1997. "Implied volatility skews and stock return skewness and kurtosis implied by stock option prices," The European Journal of Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 3(1), pages 73-85.
  13. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 25(10), pages 1457-1483, October.
  14. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 167-179.
  15. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195060119, October.
  16. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 10(3), pages 347-369, November.
  17. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 363-90, March.
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