Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices

Catherine Forbes, Gael Martin and Jonathan Wright

No 2/02, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: 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.

Keywords: Option Pricing; Stochastic Volatility; Volatility Risk; Bayesian Implicit Inference; Markov Chain Monte Carlo (search for similar items in EconPapers)
JEL-codes: C13 C51 C52 G13 (search for similar items in EconPapers)
Pages: 40 pages
Date: 2002-02
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-fmk
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Citations: View citations in EconPapers (4)

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