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Title: A Bayesian long short-term memory model for value at risk and expected shortfall joint forecasting Authors:  Zhengkun Li - The University of Sydney (Australia) [presenting]
Minh-Ngoc Tran - University of Sydney (Australia)
Richard Gerlach - University of Sydney (Australia)
Junbin Gao - The University of Sydney (Australia)
Abstract: Value at Risk (VaR) and Expected Shortfall (ES) are widely used by financial institutions to measure the market risk and avoid the extreme market movement. The proposal of Asymmetric Laplace (AL) score function allows to backtest VaR and ES forecasting accuracy jointly, as well as the joint modelling of VaR and ES by constructing the optimization problem with the AL score function entered as the underlying objective function. As the result, several linear models and their extensions were proposed. However, it is still challenging to model the possible nonlinear factors in the underlying dynamics. We address the problem by developing a Bayesian approach that can capture the nonlinear and long-term effects with the Long Short-Term Memory (LSTM) structure, a neural network approach for time series modelling. We further adapt the adaptive Markov chain Monte Carlo (MCMC) algorithm to estimate the model parameters based on the AL log likelihood function. Empirical results show that the proposed Bayesian LSTM-AL model can improve the forecasting accuracy over a range of well-established and recent proposed models, the advantages can be observable from both test results and dynamic plots.