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Bayesian Option Pricing using Asymmetric Garch Models

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  • Bauwens, L.
  • Lubrano, M.

Abstract

This paper shows how one can compute option prices from a Bayesian inference view point, using a GARCH model for the dynamics of the the volatility of the underlying asset. The proposed evaluation of an option is the predictive expectation of its payoff function. The predictive distribution of this function provides a natural metric, provided it is neutralised with respect to the risk, for gauging the predictive option price or other option evaluations. The proposed method is compared to the Black and Scholes evaluation, in which a marginal mean volatility is plugged, but which does not provide a natural metric. The methods are illustrated using symmetric, asymmetric and smooth transition GARCH models with data on a stock index in Brussels.

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Bibliographic Info

Paper provided by Universite Aix-Marseille III in its series G.R.E.Q.A.M. with number 00a18.

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Length: 23 pages
Date of creation: 2000
Date of revision:
Handle: RePEc:fth:aixmeq:00a18

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Keywords: PRICING ; EXPECTATIONS ; ECONOMETRIC MODELS;

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References

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  1. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
  2. Ronald J. Mahieu & Peter C. Schotman, 1998. "An empirical application of stochastic volatility models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(4), pages 333-360.
  3. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De.
  4. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  5. BAUWENs, Luc & LUBRANO , Michel, 1996. "Bayesian Inference on GARCH Models using the Gibbs Sampler," CORE Discussion Papers 1996027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Lubrano, M., 1999. "Smooth Transition GARCH Models: a Bayesian perspective," G.R.E.Q.A.M. 99a49, Universite Aix-Marseille III.
  7. René Garcia & Éric Renault, 1997. "A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models," CIRANO Working Papers 97s-13, CIRANO.
  8. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
  9. Jan Kallsen & Murad S. Taqqu, 1998. "Option Pricing in ARCH-type Models," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 13-26.
  10. 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.
  11. Geweke, John, 1989. "Exact predictive densities for linear models with arch disturbances," Journal of Econometrics, Elsevier, vol. 40(1), pages 63-86, January.
  12. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  13. 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.
  14. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
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Citations

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Cited by:
  1. Chiang, Min-Hsien & Huang, Hsin-Yi, 2011. "Stock market momentum, business conditions, and GARCH option pricing models," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 488-505, June.
  2. Jeroen V.K. Rombouts & Lars Stentoft, 2009. "Bayesian Option Pricing Using Mixed Normal Heteroskedasticity Models," CREATES Research Papers 2009-07, School of Economics and Management, University of Aarhus.
  3. Darsinos, T. & Satchell, S.E., 2001. "Bayesian Forecasting of Options Prices: A Natural Framework for Pooling Historical and Implied Volatiltiy Information," Cambridge Working Papers in Economics 0116, Faculty of Economics, University of Cambridge.
  4. David Ardia & Lennart F. Hoogerheide, 2010. "Efficient Bayesian Estimation and Combination of GARCH-Type Models," Tinbergen Institute Discussion Papers 10-046/4, Tinbergen Institute.
  5. Ausin, Maria Concepcion & Galeano, Pedro, 2007. "Bayesian estimation of the Gaussian mixture GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2636-2652, February.
  6. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Ardia, David & Hoogerheide, Lennart F., 2010. "Efficient Bayesian estimation and combination of GARCH-type models," MPRA Paper 22919, University Library of Munich, Germany.
  8. Giannikis, D. & Vrontos, I.D. & Dellaportas, P., 2008. "Modelling nonlinearities and heavy tails via threshold normal mixture GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1549-1571, January.
  9. Ehlers, Ricardo S., 2012. "Computational tools for comparing asymmetric GARCH models via Bayes factors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 858-867.
  10. Kiyotaka Satoyoshi & Hidetoshi Mitsui, 2011. "Empirical Study of Nikkei 225 Options with the Markov Switching GARCH Model," Asia-Pacific Financial Markets, Springer, vol. 18(1), pages 55-68, March.
  11. Lanne, Markku & Luoto, Jani, 2008. "Robustness of the risk-return relationship in the U.S. stock market," Finance Research Letters, Elsevier, vol. 5(2), pages 118-127, June.
  12. Shu Wing Ho & Alan Lee & Alastair Marsden, 2011. "Use of Bayesian Estimates to determine the Volatility Parameter Input in the Black-Scholes and Binomial Option Pricing Models," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 4(1), pages 74-96, December.
  13. Rombouts, Jeroen V.K. & Stentoft, Lars, 2014. "Bayesian option pricing using mixed normal heteroskedasticity models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 588-605.

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