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Parametric Pricing of Higher Order Moments in S&P500 Options

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  • G.C. Lim
  • G.M. Martin

    ()

  • V.L. Martin

Abstract

A general parametric framework is developed for pricing S&P500 options. Skewness and leptokurtosis in stock returns as well as time-varying volatility are priced. The parametric pricing model nests the Black-Scholes model and can explain volatility smiles and skews in stock options. The data consist of S&P500 options traded on select days in April, 1995, a total sample of over 500,000 observations. A number of performance criteria are used to evaluate the alternative models. The empirical results show that pricing higher order moments yield improvements in the pricing of options over the Black-Scholes model as well as other models.

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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 1/02.

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Length: 47 pages
Date of creation: Feb 2002
Date of revision:
Handle: RePEc:msh:ebswps:2002-1

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Keywords: Option Pricing; Volatility Smiles and Skews; Generalized Student t; Skewness; Kurtosis; Time-Varying Volatility.;

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References

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  2. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
  3. Gael M. Martin & Catherine S. Forbes & Vance L. Martin, 2005. "Implicit Bayesian Inference Using Option Prices," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 437-462, 05.
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  11. 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.
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  15. Lim, G. C. & Lye, J. N. & Martin, G. M. & Martin*, V. L., 1998. "The distribution of exchange rate returns and the pricing of currency options," Journal of International Economics, Elsevier, vol. 45(2), pages 351-368, August.
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Citations

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Cited by:
  1. Ryszard Kokoszczyński & Paweł Sakowski & Robert Ślepaczuk, 2010. "Midquotes or Transactional Data? The Comparison of Black Model on HF Data," Working Papers 2010-15, Faculty of Economic Sciences, University of Warsaw.
  2. Ángel León & Javier Mencía & Enrique Sentana, 2007. "Parametric properties of semi-nonparametric distributions, with applications to option valuation," Banco de Espa�a Working Papers 0707, Banco de Espa�a.
  3. Ng, Jason & Forbes, Catherine S. & Martin, Gael M. & McCabe, Brendan P.M., 2013. "Non-parametric estimation of forecast distributions in non-Gaussian, non-linear state space models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 411-430.
  4. Maasoumi, Esfandiar & Lim, G.C. & Martin, Vance, 2006. "A reexamination of the equity-premium puzzle: A robust non-parametric approach," Departmental Working Papers 0604, Southern Methodist University, Department of Economics.
  5. Gael M. Martin & Andrew Reidy & Jill Wright, 2007. "Does the Option Market Produce Superior Forecasts of Noise-Corrected Volatility Measures?," Monash Econometrics and Business Statistics Working Papers 5/07, Monash University, Department of Econometrics and Business Statistics.
  6. Emese Lazar & Carol Alexander, 2006. "Normal mixture GARCH(1,1): applications to exchange rate modelling," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 307-336.
  7. Lim, G.C. & Martin, G.M. & Martin, V.L., 2006. "Pricing currency options in the presence of time-varying volatility and non-normalities," Journal of Multinational Financial Management, Elsevier, vol. 16(3), pages 291-314, July.
  8. Gael M. Martin & Andrew Reidy & Jill Wright, 2006. "Assessing the Impact of Market Microstructure Noise and Random Jumps on the Relative Forecasting Performance of Option-Implied and Returns-Based Volatility," Monash Econometrics and Business Statistics Working Papers 10/06, Monash University, Department of Econometrics and Business Statistics.
  9. Vance Martin & G.C. Lim & Esfandiar Maasoumi, 2004. "Discounting The Equity Premium Puzzle," Econometric Society 2004 Australasian Meetings 331, Econometric Society.
  10. Ryszard Kokoszczyński & Paweł Sakowski & Robert Ślepaczuk, 2010. "Which Option Pricing Model is the Best? High Frequency Data for Nikkei225 Index Options," Working Papers 2010-16, Faculty of Economic Sciences, University of Warsaw.

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