Inference for a Class of Stochastic Volatility Models Using Option and Spot Prices: Application of a Bivariate Kalman Filter

Catherine Forbes, Gael Martin and Jill Wright

Econometric Reviews, 2007, vol. 26, issue 2-4, 387-418

Abstract: In this paper Bayesian methods are applied to a stochastic volatility model using both the prices of the asset and the prices of options written on the asset. Posterior densities for all model parameters, latent volatilities and the market price of volatility risk are produced via a Markov Chain Monte Carlo (MCMC) sampling algorithm. Candidate draws for the unobserved volatilities are obtained in blocks by applying the Kalman filter and simulation smoother to a linearization of a nonlinear state space representation of the model. Crucially, information from both the spot and option prices affects the draws via the specification of a bivariate measurement equation, with implied Black-Scholes volatilities used to proxy observed option prices in the candidate model. Alternative models nested within the Heston (1993) framework are ranked via posterior odds ratios, as well as via fit, predictive and hedging performance. The method is illustrated using Australian News Corporation spot and option price data.

Keywords: Bayesian inference; Markov Chain Monte Carlo; Multi-move sampler; Option pricing; Nonlinear state space model; Volatility risk (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (14)

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DOI: 10.1080/07474930701220584

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