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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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    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. 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 de Valor Público 15923, Universidad EAFIT.
    3. Arismendi, Juan & Genaro, Alan De, 2016. "A Monte Carlo multi-asset option pricing approximation for general stochastic processes," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 75-99.
    4. Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Revisited Multi-moment Approximate Option," FMG Discussion Papers dp430, Financial Markets Group.
    5. 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.
    6. Juan Arismendi, 2014. "A Multi-Asset Option Approximation for General Stochastic Processes," ICMA Centre Discussion Papers in Finance icma-dp2014-03, Henley Business School, University of Reading.
    7. Catherine S. Forbes & Gael M. Martin & Jill Wright, 2007. "Inference for a Class of Stochastic Volatility Models Using Option and Spot Prices: Application of a Bivariate Kalman Filter," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 387-418.
    8. 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.
    9. 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.
    10. Nizar Riane, 2023. "The inverse Black-Scholes problem in Radon measures space revisited: towards a new measure of market uncertainty," Papers 2303.16773, arXiv.org.
    11. J. C. Arismendi & Marcel Prokopczuk, 2016. "A moment-based analytic approximation of the risk-neutral density of American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(6), pages 409-444, November.
    12. Monica Billio & Bertrand Maillet & Loriana Pelizzon, 2022. "A meta-measure of performance related to both investors and investments characteristics," Annals of Operations Research, Springer, vol. 313(2), pages 1405-1447, June.
    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. Vance Martin & G.C. Lim & Esfandiar Maasoumi, 2004. "Discounting The Equity Premium Puzzle," Econometric Society 2004 Australasian Meetings 331, Econometric Society.
    15. 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.
    16. 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.
    17. 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.
    18. Nizar Riane & Claire David, 2024. "Generalized measure Black-Scholes equation: Towards option self-similar pricing," Papers 2404.05214, arXiv.org.
    19. 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.
    20. Gael M. Martin & David T. Frazier & Worapree Maneesoonthorn & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2022. "Bayesian Forecasting in Economics and Finance: A Modern Review," Papers 2212.03471, arXiv.org, revised Jul 2023.
    21. 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.
    22. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    23. 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.
    24. 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.
    25. Cortés, Lina M. & Mora-Valencia, Andrés & Perote, Javier, 2020. "Retrieving the implicit risk neutral density of WTI options with a semi-nonparametric approach," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).

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    More about this item

    Keywords

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

    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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