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

Author

Listed:
  • 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.

Suggested Citation

  • Ángel León & Javier Mencía & Enrique Sentana, 2007. "Parametric properties of semi-nonparametric distributions, with applications to option valuation," Working Papers 0707, Banco de España;Working Papers Homepage.
  • Handle: RePEc:bde:wpaper:0707
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    References listed on IDEAS

    as
    1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    2. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Skewness and kurtosis implied by option prices: a second comment," LSE Research Online Documents on Economics 24938, London School of Economics and Political Science, LSE Library.
    3. 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, vol. 3(1), pages 73-85.
    4. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31 World Scientific Publishing Co. Pte. Ltd..
    5. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    6. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    7. 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.
    8. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    9. 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.
    10. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    11. Ronald Gallant, A. & Tauchen, George, 1999. "The relative efficiency of method of moments estimators1," Journal of Econometrics, Elsevier, vol. 92(1), pages 149-172, September.
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    13. 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.
    14. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
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    More about this item

    Keywords

    kurtosis; density expansions; gram-charlier; skewness; s&p index options;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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