Parametric Properties of Semi-Nonparametric Distributions, With Applications to Option Valuation
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 general than the truncated Gram-Charlier expansions of Jondeau and Rockinger (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 the truncated expansions.
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- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- 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, 06.
- 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.
- Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
- 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.
- BONTEMPS, Christian & MEDDAHI, Nour, 2002.
"Testing Normality : A GMM Approach,"
Cahiers de recherche
2002-14, Universite de Montreal, Departement de sciences economiques.
- 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.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, March.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
- 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.
- 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.
- Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
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