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

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  • Catherine S. Forbes
  • Gael M. Martin
  • Jill Wright

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.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 26 (2007)
Issue (Month): 2-4 ()
Pages: 387-418

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Handle: RePEc:taf:emetrv:v:26:y:2007:i:2-4:p:387-418

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Related research

Keywords: Bayesian inference; Markov Chain Monte Carlo; Multi-move sampler; Option pricing; Nonlinear state space model; Volatility risk;

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Cited by:
  1. Gael M. Martin & Andrew Reidy & Jill Wright, 2007. "Does the Option Market Produce Superior Forecasts of Noise-Corrected Volatility Measures?," Monash Econometrics and Business Statistics Working Papers 5/07, Monash University, Department of Econometrics and Business Statistics.
  2. Worapree Maneesoonthorn & Gael M. Martin & Catherine S. Forbes & Simone Grose, 2010. "Probabilistic Forecasts of Volatility and its Risk Premia," Monash Econometrics and Business Statistics Working Papers 22/10, Monash University, Department of Econometrics and Business Statistics.
  3. repec:qut:auncer:2012_11 is not listed on IDEAS
  4. Shu Wing Ho & Alan Lee & Alastair Marsden, 2011. "Use of Bayesian Estimates to determine the Volatility Parameter Input in the Black-Scholes and Binomial Option Pricing Models," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 4(1), pages 74-96, December.

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