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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