Parametric Properties Of Semi-Nonparametric Distributions, With Applications To Option Valuation
AbstractWe derive the statistical properties of the SNP densities of Gallant and Nychka (1987). We show that these densities, which are always positive, are more general than the truncated Gram-Charlier expansions of Jondeau and Rochinger (2001), who impose parameter restrictions to ensure positivity. We also use the SNP densities for option valuation. We relate real and risk-neutral measures, obtain closed-form prices for European options, and study the "Greeks". We show that SNP densities generate wider option price ranges than the truncated expansions. In an empirical application to S&P 500 index options, we find that the SNP model beats the standard and Practitioner's Black-Scholes formulas, and truncated expansions.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by CEMFI in its series Working Papers with number wp2005_0509.
Date of creation: Dec 2005
Date of revision:
Kurtosis; density expansions; Gram-Charlie; skewness; S&P index options.;
Other versions of this item:
- LeÃ³n, Ãngel & MencÃa, Javier & Sentana, Enrique, 2009. "Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 176-192.
- Ángel León & Javier Mencía & Enrique Sentana, 2007. "Parametric properties of semi-nonparametric distributions, with applications to option valuation," Banco de Espaï¿½a Working Papers 0707, Banco de Espa�a.
- León, Ángel & Mencía, Javier & Sentana, Enrique, 2005. "Parametric Properties of Semi-Nonparametric Distributions, With Applications to Option Valuation," CEPR Discussion Papers 5435, C.E.P.R. Discussion Papers.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-09-11 (All new papers)
- NEP-FIN-2006-09-11 (Finance)
- NEP-FMK-2006-09-11 (Financial Markets)
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.:
- Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
- 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 621-51, October.
- 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.
- Emmanuel Jurczenko & Bertrand Maillet & Bogdan Negrea, 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.
- Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Skewness and Kurtosis Implied by Option Prices: A Second Comment," FMG Discussion Papers dp419, Financial Markets Group.
- Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006.
"Pricing and Inference with Mixtures of Conditionally Normal Processes,"
2006-28, Centre de Recherche en Economie et Statistique.
- Bertholon, H. & Monfort, A. & Pegoraro, F., 2007. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working papers 188, Banque de France.
- 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.
- Christian Bontemps & Nour Meddahi, 2002.
"Testing Normality: A GMM Approach,"
CIRANO Working Papers
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
- 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.
- G.C. Lim & G.M. Martin & V.L. Martin, 2002. "Parametric Pricing of Higher Order Moments in S&P500 Options," Monash Econometrics and Business Statistics Working Papers 1/02, Monash University, Department of Econometrics and Business Statistics.
- Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
- 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.
- 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, vol. 19(2), pages 175-92, Summer.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- 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.
- Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
- 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.
- Victor Fenton & Gallant, A. Ronald, 1996.
"Qualitative and Asymptotic Performance of SNP Density Estimators,"
96-17, Duke University, Department of Economics.
- 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.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Araceli Requerey).
If references are entirely missing, you can add them using this form.