Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices
In 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.
|Date of creation:||Feb 2002|
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- 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.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985.
"A Theory of the Term Structure of Interest Rates,"
Econometric Society, vol. 53(2), pages 385-407, March.
- 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.
- 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.
- Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
- 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.
- 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.
- 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.
- 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.
- repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
- Chib, Siddhartha & Greenberg, Edward, 1996.
"Markov Chain Monte Carlo Simulation Methods in Econometrics,"
Cambridge University Press, vol. 12(03), pages 409-431, August.
- Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics 9408001, EconWPA, revised 24 Oct 1994.
- 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.
- 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.
- Gael Martin, 2001. "Bayesian Analysis Of A Fractional Cointegration Model," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 217-234.
- 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.
- 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.
- 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.
- 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.
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