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

Taras Bodnar, Vilhelm Niklasson and Erik Thorsén

Abstract

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.