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Parametric pricing of higher order moments in S&P500 options

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Author Info

  • V. L. Martin

    (Department of Economics, University of Melbourne, Australia)

  • G. M. Martin

    (Department of Econometrics and Business Statistics, Monash University, Australia)

  • G. C. Lim

    (Department of Economics, University of Melbourne, Australia)

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.

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File URL: http://hdl.handle.net/10.1002/jae.762
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File URL: http://qed.econ.queensu.ca:80/jae/2005-v20.3/
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Bibliographic Info

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 20 (2005)
Issue (Month): 3 ()
Pages: 377-404

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Handle: RePEc:jae:japmet:v:20:y:2005:i:3:p:377-404

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References

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  1. 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.
  2. 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.
  3. Hafner, Christian M. & Herwartz, Helmut, 1999. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," SFB 373 Discussion Papers 1999,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  4. Martin, G.M. & Forbes, C.S. & Martin, V.L., 2000. "Implicit Bayesian Inference Using Option Prices," Monash Econometrics and Business Statistics Working Papers 5/00, Monash University, Department of Econometrics and Business Statistics.
  5. 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.
  6. 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, 04.
  7. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
  8. 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.
  9. 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.
  10. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  11. Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  17. Joshua V. Rosenberg & Robert F. Engle, 1997. "Option Hedging Using Empirical Pricing Kernels," NBER Working Papers 6222, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. Vance Martin & G.C. Lim & Esfandiar Maasoumi, 2004. "Discounting The Equity Premium Puzzle," Econometric Society 2004 Australasian Meetings 331, Econometric Society.
  2. 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.
  3. 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.
  4. 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.
  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. 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. 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.
  8. Ángel León & Javier Mencía & Enrique Sentana, 2005. "Parametric Properties Of Semi-Nonparametric Distributions, With Applications To Option Valuation," Working Papers wp2005_0509, CEMFI.
  9. 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.
  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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