Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices
AbstractIn this paper we apply Bayesian methods to estimate a stochastic volatility model using both the prices of the asset and the prices of options written on the asset. Implicit posterior densities for the parameters of the volatility model, for the latent volatilities and for the market price of volatility risk are produced. The method involves augmenting the data generating process associated with a panel of option prices with the probability density function describing the dynamics of the underlying bivariate spot price and volatility process. Posterior results are produced via a hybrid Markov Chain Monte Carlo sampling algorithm. Candidate draws which assume a given dynamic process for the volatility are re-weighted according to the information in both the option and spot price data. The method is illustrated using the Heston (1993) stochastic volatility model, based on data simulated to mimic the features of recent S&P500 spot and option price data. The way in which alternative option pricing models can be ranked, via Bayes Factors and via fit, predictive and hedging performance, is demonstrated.
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Bibliographic InfoPaper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 2/02.
Length: 40 pages
Date of creation: Feb 2002
Date of revision:
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Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Web page: http://www.buseco.monash.edu.au/depts/ebs/
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Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-04-25 (All new papers)
- NEP-ECM-2002-04-25 (Econometrics)
- NEP-ETS-2002-04-25 (Econometric Time Series)
- NEP-FMK-2002-04-25 (Financial Markets)
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- 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.
- Martin, G.M., 1998.
"U.S. Deficit Sustainability: A New Approach Based on Multiple Endogenous Breaks,"
Monash Econometrics and Business Statistics Working Papers
1/98, Monash University, Department of Econometrics and Business Statistics.
- Gael M. Martin, 2000. "US deficit sustainability: a new approach based on multiple endogenous breaks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(1), pages 83-105.
- 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.
- 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.
- 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.
- Gael Martin, 2001. "Bayesian Analysis Of A Fractional Cointegration Model," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 217-234.
- 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.
- Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August.
- Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
- 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.
- Siddhartha Chib & Edward Greenberg, 1994.
"Markov Chain Monte Carlo Simulation Methods in Econometrics,"
9408001, EconWPA, revised 24 Oct 1994.
- Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
- Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November.
- repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
- Guo, Dajiang, 1998. "The Risk Premium of Volatility Implicit in Currency Options," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 498-507, October.
- 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.
- Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
- Cappuccio Nunzio & Lubian Diego & Raggi Davide, 2004.
"MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model,"
Studies in Nonlinear Dynamics & Econometrics,
De Gruyter, vol. 8(2), pages 1-31, May.
- Nunzio Cappuccio & Diego Lubian & Davide Raggi, 2003. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatily Model," Working Papers 7, University of Verona, Department of Economics.
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