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Bayesian estimates of VaR using GM(1,1)-POT-VaR model

Author(s): Wang Jin, Wang Ruiqing

Electricity price connotes a grey system, due to uncertainty and incomplete information for partial external or inner parameters. A two-stage method based on grey system and extreme value theory is proposed to estimate the value-at-risk. In stage one, to capture the dependencies, seasonalities and volatility-clustering, a gray GM(1,1) model is utilized to filter electricity price series. In this way, an approximately independently and identically distributed residual series with better statistical properties is acquired. In stage two, a peaks over threshold method is adopted to explicitly model the tails of the residuals of GM(1,1) model, and accurate estimates of electricity market value-at-risk can be produced. For conquering the difficulty of lacking observed data over threshold, Bayesian estimation based on Markov Chain Monte Carlo simulation is used to estimate the parameters of peaks over threshold model. The empirical analysis shows that the proposed model can be rapidly reflect the most recent and relevant changes of electricity prices and produce accurate forecasts of value-at-risk at all confidence levels, and the computational cost is far less than the existing two-stage value-at-risk estimating models, further improving the ability of risk management for electricity market participants.

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