Journal of Risk

Volatility-sensitive Bayesian estimation of portfolio value-at-risk and conditional value-at-risk

Taras Bodnar, Vilhelm Niklasson and Erik Thorsén

  • A novel Bayesian method for integrating volatility information when estimating value-at-risk and conditional value-at-risk is introduced.
  • The model utilizes a conjugate prior and proposes an automatic method to specify hyperparameters, accounting for volatility clustering.
  • Theoretical results illustrating the behavior of the new estimate are derived.
  • The efficacy our the new approach is demonstrated using both simulated and empirical data, highlighting its strength in risk estimation during volatile market conditions.

We suggest a new method for integrating volatility information for estimating the value-at-risk and conditional value-at-risk of a portfolio. This new method is developed from the perspective of Bayesian statistics and is based on the idea of volatility clustering. By specifying the hyperparameters in a conjugate prior based on two different rolling window sizes, it is possible to quickly adapt to changes in volatility and automatically specify the degree of certainty in the prior. This gives our method an advantage over existing Bayesian methods, which are less sensitive to such changes in volatilities and usually lack standardized ways of expressing the degree of belief. We illustrate our new approach using both simulated and empirical data. The new method provides a good alternative to other well-known homoscedastic and heteroscedastic models for risk estimation, especially during turbulent periods, when it can quickly adapt to changing market conditions.

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