IDEAS home Printed from https://ideas.repec.org/a/wly/japmet/v20y2005i3p377-404.html
   My bibliography  Save this article

Parametric pricing of higher order moments in S&P500 options

Author

Listed:
  • G. C. Lim
  • G. M. Martin
  • V. L. Martin

Abstract

A general parametric framework based on the generalized Student t‐distribution is developed for pricing S&P500 options. Higher order moments in stock returns as well as time‐varying volatility are priced. An important computational advantage of the proposed framework over Monte Carlo‐based pricing methods is that options can be priced using one‐dimensional quadrature integration. The empirical application is based on S&P500 options traded on select days in April 1995, a total sample of over 100,000 observations. A range of performance criteria are used to evaluate the proposed model, as well as a number of alternative models. The empirical results show that pricing higher order moments and time‐varying volatility yields improvements in the pricing of options, as well as correcting the volatility skew associated with the Black–Scholes model. Copyright © 2004 John Wiley & Sons, Ltd.

Suggested Citation

  • G. C. Lim & G. M. Martin & V. L. Martin, 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, March.
  • Handle: RePEc:wly:japmet:v:20:y:2005:i:3:p:377-404
    DOI: 10.1002/jae.762
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/jae.762
    Download Restriction: no

    File URL: https://libkey.io/10.1002/jae.762?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ms. Jenny N. Lye, 1998. "Parametric Distributional Flexibility and Conditional Variance Models with an Application to Hourly Exchange Rates," IMF Working Papers 1998/029, International Monetary Fund.
    2. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    3. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    4. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    5. Jacquier, Eric & Jarrow, Robert, 2000. "Bayesian analysis of contingent claim model error," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 145-180.
    6. Clement, E. & Gourieroux, C. & Monfort, A., 2000. "Econometric specification of the risk neutral valuation model," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 117-143.
    7. Rosenberg, Joshua V., 1998. "Pricing multivariate contingent claims using estimated risk-neutral density functions," Journal of International Money and Finance, Elsevier, vol. 17(2), pages 229-247, April.
    8. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    9. 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.
    10. Catherine S. Forbes & Gael M. Martin & Jill Wright, 2003. "Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices: Application of a Bivariate Kalman Filter," Monash Econometrics and Business Statistics Working Papers 17/03, Monash University, Department of Econometrics and Business Statistics.
    11. Bauwens, Luc & Lubrano, Michel, 2002. "Bayesian option pricing using asymmetric GARCH models," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 321-342, August.
    12. 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, March.
    13. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
    14. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    15. Melick, William R. & Thomas, Charles P., 1997. "Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(1), pages 91-115, March.
    16. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    17. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 1-34, March.
    18. 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.
    19. Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
    20. Thierry Ané, 1999. "Pricing and hedging S&P 500 index options with Hermite polynomial approximation: empirical tests of Madan and Milne's model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(7), pages 735-758, October.
    21. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    22. Garcia, Rene & Gencay, Ramazan, 2000. "Pricing and hedging derivative securities with neural networks and a homogeneity hint," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 93-115.
    23. 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.
    24. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    25. Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
    26. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    27. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    28. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    29. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
    30. 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 637-654, May-June.
    31. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    32. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    33. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, April.
    34. Joshua V. Rosenberg & Robert F. Engle, 1997. "Option Hedging Using Empirical Pricing Kernels," NBER Working Papers 6222, National Bureau of Economic Research, Inc.
    35. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    36. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Vance Martin & G.C. Lim & Esfandiar Maasoumi, 2004. "Discounting The Equity Premium Puzzle," Econometric Society 2004 Australasian Meetings 331, Econometric Society.
    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. 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.
    7. Nizar Riane & Claire David, 2024. "Generalized measure Black-Scholes equation: Towards option self-similar pricing," Papers 2404.05214, arXiv.org.
    8. Carol Alexander & Emese Lazar, 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, April.
    9. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Revisited Multi-moment Approximate Option," FMG Discussion Papers dp430, Financial Markets Group.
    19. 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.
    20. 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.
    21. 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).
    22. 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.
    23. 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.
    24. 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.
    25. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    4. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    5. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    6. Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Revisited Multi-moment Approximate Option," FMG Discussion Papers dp430, Financial Markets Group.
    7. René Garcia & Richard Luger & Eric Renault, 2001. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables (Note : Nouvelle version Février 2002)," CIRANO Working Papers 2001s-02, CIRANO.
    8. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    9. 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.
    10. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, vol. 50(9), pages 1204-1221, September.
    11. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    12. Garcia, Rene & Luger, Richard & Renault, Eric, 2003. "Empirical assessment of an intertemporal option pricing model with latent variables," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 49-83.
    13. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
    14. Rubio Irigoyen, Gonzalo & Ferreira García, María Eva & Gago, Mónica & León, Angel, 2002. "An empirical comparison of the performance of alternative option pricing models," DFAEII Working Papers 1988-088X, University of the Basque Country - Department of Foundations of Economic Analysis II.
    15. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    16. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    17. Lin, Shin-Hung & Huang, Hung-Hsi & Li, Sheng-Han, 2015. "Option pricing under truncated Gram–Charlier expansion," The North American Journal of Economics and Finance, Elsevier, vol. 32(C), pages 77-97.
    18. Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, vol. 72(2), pages 291-318, May.
    19. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    20. Byun, Suk Joon & Jeon, Byoung Hyun & Min, Byungsun & Yoon, Sun-Joong, 2015. "The role of the variance premium in Jump-GARCH option pricing models," Journal of Banking & Finance, Elsevier, vol. 59(C), pages 38-56.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:japmet:v:20:y:2005:i:3:p:377-404. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0883-7252/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.