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A Closed-Form GARCH Option Valuation Model

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Author Info
Heston, Steven L
Nandi, Saikat
Abstract

This paper develops a closed-form option valuation formula for a spot asset whose variance follows a GARCH(p, q) process that can be correlated with the returns of the spot asset. It provides the first readily computed option formula for a random volatility model that can be estimated and implemented solely on the basis of observables. The single lag version of this model contains Heston's (1993) stochastic volatility model as a continuous-time limit. Empirical analysis on S&P500 index options shows that the out-of-sample valuation errors from the single lag version of the GARCH model are substantially lower than the ad hoc Black-Scholes model of Dumas, Fleming and Whaley (1998) that uses a separate implied volatility for each option to fit to the smirk/smile in implied volatilities. The GARCH model remains superior even though the parameters of the GARCH model are held constant and volatility is filtered from the history of asset prices while the ad hoc Black-Scholes model is updated every period. The improvement is largely due to the ability of the GARCH model to simultaneously capture the correlation of volatility, with spot returns and the path dependence in volatility. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

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Publisher Info
Article provided by Oxford University Press for Society for Financial Studies in its journal Review of Financial Studies.

Volume (Year): 13 (2000)
Issue (Month): 3 ()
Pages: 585-625
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Handle: RePEc:oup:rfinst:v:13:y:2000:i:3:p:585-625

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  1. Peter C.B. Phillips & Jun Yu, 2007. "Simulation-based Estimation of Contingent-claims Prices," Cowles Foundation Discussion Papers 1596, Cowles Foundation, Yale University. [Downloadable!]
  2. Guidolin, Massimo & Timmermann, Allan G, 2001. "Option Prices under Bayesian Learning: Implied Volatility Dynamics and Predictive Densities," CEPR Discussion Papers 3005, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  3. Rene Garcia & Richard Luger & Eric Renault, 2004. "Option Prices, Preferences, and State Variables," Emory Economics 0418, Department of Economics, Emory University (Atlanta). [Downloadable!]
  4. Giovanni Barone-Adesi & Robert Engle & Loriano Mancini, 2006. "GARCH Options in Incomplete Markets," CEI Working Paper Series 2005-12, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
  5. Peter Christoffersen & Francis X. Diebold, 2002. "Financial Asset Returns, Market Timing, and Volatility Dynamics," CIRANO Working Papers 2002s-02, CIRANO. [Downloadable!]
  6. V. L. Martin & G. M. Martin & G. C. Lim, 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. [Downloadable!]
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  7. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO. [Downloadable!]
  8. Daal, Elton & Naka, Atsuyuki & Yu, Jung-Suk, 2004. "Volatility clustering, leverage effects, and jumps dynamics in emerging Asian equity markets," Working Papers 2004-05, University of New Orleans, Department of Economics and Finance. [Downloadable!]
  9. 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. [Downloadable!]
  10. Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C, 2005. "Loss Functions in Option Valuation: A Framework for Model Selection," CEPR Discussion Papers 4960, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  11. Peter F. Christoffersen & Francis X. Diebold, 2003. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," NBER Working Papers 10009, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. Gonzalo Rubio & Eva Ferreira & Mónica Gago, 2003. "An empirical comparison of the performance of alternative option pricing models," DFAEII Working Papers 200204, University of the Basque Country - Department of Foundations of Economic Analysis II. [Downloadable!]
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  13. Francesco Audrino & Dominik Colagelo, 2007. "Forecasting Implied Volatility Surfaces," University of St. Gallen Department of Economics working paper series 2007 2007-42, Department of Economics, University of St. Gallen. [Downloadable!]
  14. René Garcia & Richard Luger & Éric Renault, 2001. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables (Note : New version February 2002) / Empirical Assessment of an Intertemporal Option Pricing Model with Latent Varia," CIRANO Working Papers 2001s-02, CIRANO. [Downloadable!]
  15. Angel León & Gonzalo Rubio & Gregorio Serna, 2003. "Autorregresive conditional volatility, skewness and kurtosis," DFAEII Working Papers 200206, University of the Basque Country - Department of Foundations of Economic Analysis II. [Downloadable!]
  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. [Downloadable!]
  17. Gael M. Martin & Catherine S. Forbes & Vance L. Martin, 2003. "Implicit Bayesian Inference Using Option Prices," Monash Econometrics and Business Statistics Working Papers 5/03, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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  18. Takayuki Shiohama, 2006. "Asymptotically Efficient Estimation of the Change Point for Semiparametric GARCH models," Discussion Paper Series a471, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
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