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Probabilistic forecasts of volatility and its risk premia

Author

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  • Maneesoonthorn, Worapree
  • Martin, Gael M.
  • Forbes, Catherine S.
  • Grose, Simone D.
Abstract
The object of this paper is to produce distributional forecasts of asset price volatility and its associated risk premia using a non-linear state space approach. Option and spot market information on the latent variance process is captured by using dual ‘model-free’ variance measures to define a bivariate observation equation in the state space model. The premium for variance diffusive risk is defined as linear in the latent variance (in the usual fashion) whilst the premium for variance jump risk is specified as a conditionally deterministic dynamic process, driven by a function of past measurements. The inferential approach adopted is Bayesian, implemented via a Markov chain Monte Carlo algorithm that caters for the multiple sources of non-linearity in the model and for the bivariate measure. The method is applied to spot and option price data on the S&P500 index from 1999 to 2008, with conclusions drawn about investors’ required compensation for variance risk during the recent financial turmoil. The accuracy of the probabilistic forecasts of the observable variance measures is demonstrated, and compared with that of forecasts yielded by alternative methods. To illustrate the benefits of the approach, it is used to produce forecasts of prices of derivatives on volatility itself. In addition, the posterior distribution is augmented by information on daily returns to produce value at risk predictions. Linking the variance risk premia to the risk aversion parameter in a representative agent model, probabilistic forecasts of (approximate) relative risk aversion are also produced.

Suggested Citation

  • Maneesoonthorn, Worapree & Martin, Gael M. & Forbes, Catherine S. & Grose, Simone D., 2012. "Probabilistic forecasts of volatility and its risk premia," Journal of Econometrics, Elsevier, vol. 171(2), pages 217-236.
    • Handle: RePEc:eee:econom:v:171:y:2012:i:2:p:217-236
    DOI: 10.1016/j.jeconom.2012.06.006
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    3. David Harris & Gael M. Martin & Indeewara Perera & Don S. Poskitt, 2017. "Construction and visualization of optimal confidence sets for frequentist distributional forecasts," Monash Econometrics and Business Statistics Working Papers 9/17, Monash University, Department of Econometrics and Business Statistics.
    4. Worapree Maneesoonthorn & Gael M Martin & Catherine S Forbes, 2018. "Dynamic price jumps: The performance of high frequency tests and measures, and the robustness of inference," Monash Econometrics and Business Statistics Working Papers 17/18, Monash University, Department of Econometrics and Business Statistics.
    5. Yuru Sun & Worapree Maneesoonthorn & Ruben Loaiza-Maya & Gael M. Martin, 2023. "Optimal probabilistic forecasts for risk management," Papers 2303.01651, arXiv.org.
    6. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    7. Ng, Jason & Forbes, Catherine S. & Martin, Gael M. & McCabe, Brendan P.M., 2013. "Non-parametric estimation of forecast distributions in non-Gaussian, non-linear state space models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 411-430.
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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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