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 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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Bibliographic InfoPaper provided by Banco de Espa�a in its series Banco de Espa�a Working Papers with number 0707.
Length: 60 pages
Date of creation: Mar 2007
Date of revision:
kurtosis; density expansions; gram-charlier; 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, American Statistical Association, vol. 27(2), pages 176-192.
- Ángel León & Javier Mencía & Enrique Sentana, 2005. "Parametric Properties Of Semi-Nonparametric Distributions, With Applications To Option Valuation," Working Papers, CEMFI wp2005_0509, CEMFI.
- León, Ángel & Mencía, Javier & Sentana, Enrique, 2005. "Parametric Properties of Semi-Nonparametric Distributions, With Applications to Option Valuation," CEPR Discussion Papers, C.E.P.R. 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
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- 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.
- 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.
- Victor Fenton & Gallant, A. Ronald, 1996. "Qualitative and Asymptotic Performance of SNP Density Estimators," Working Papers, Duke University, Department of Economics 96-17, Duke University, Department of Economics.
- 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.
- 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.
- 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, Monash University, Department of Econometrics and Business Statistics 1/02, Monash University, Department of Econometrics and Business Statistics.
- 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.
- 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.
- Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers, Centre de Recherche en Economie et Statistique 2006-28, Centre de Recherche en Economie et Statistique.
- 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.
- Emmanuel Jurczenko & Bertrand Maillet & Bogdan Negrea, 2002. "Skewness and kurtosis implied by option prices: a second comment," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 24938, London School of Economics and Political Science, LSE Library.
- 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.
- 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.
- 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.
- 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.
- 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.
- Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 25(10), pages 1457-1483, October.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 167-179.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195060119, October.
- 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.
- 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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