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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.

Suggested Citation

  • 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.
  • Handle: RePEc:msh:ebswps:2002-1
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    References listed on IDEAS

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    5. 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, May.
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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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    Cited by:

    1. 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.
    2. Vance Martin & G.C. Lim & Esfandiar Maasoumi, 2004. "Discounting The Equity Premium Puzzle," Econometric Society 2004 Australasian Meetings 331, Econometric Society.
    3. León, à ngel & Mencía, 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.
    4. 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.
    5. Lim, G.C. & Maasoumi, Esfandiar & Martin, Vance L., 2006. "A reexamination of the equity-premium puzzle: A robust non-parametric approach," The North American Journal of Economics and Finance, Elsevier, vol. 17(2), pages 173-189, August.
    6. Gael M. Martin & Andrew Reidy & Jill Wright, 2009. "Does the option market produce superior forecasts of noise-corrected volatility measures?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 77-104.
    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 & Brendan P.M. McCabe & Worapree Maneesoonthorn & Christian P. Robert, 2014. "Approximate Bayesian Computation in State Space Models," Monash Econometrics and Business Statistics Working Papers 20/14, Monash University, Department of Econometrics and Business Statistics.
    9. 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.
    10. Lina M. Cortés & Javier Perote & Andrés Mora-Valencia, 2017. "Implicit probability distribution for WTI options: The Black Scholes vs. the semi-nonparametric approach," DOCUMENTOS DE TRABAJO CIEF 015923, UNIVERSIDAD EAFIT.
    11. Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Revisited Multi-moment Approximate Option," FMG Discussion Papers dp430, Financial Markets Group.
    12. León, à ngel & Mencía, 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.
    13. 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.
    14. 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.
    15. Juan Arismendi, 2014. "A Multi-Asset Option Approximation for General Stochastic Processes," ICMA Centre Discussion Papers in Finance icma-dp2014-03, Henley Business School, Reading University.
    16. Fry-McKibbin, Renée & Martin, Vance L. & Tang, Chrismin, 2014. "Financial contagion and asset pricing," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 296-308.

    More about this item

    Keywords

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

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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