Abstract:

Timely and accurate forecasting of risks has always been a core issue in the finance. To this end， by making full use of transaction information and taking the discrete stochastic processes to characterize the evolution of risk， a state-space model has been established under the quantile analysis framework in this paper. In order to overcome the difficulty of parameter estimation and make the proposed model have practical value， a new algorithm is constructed in the framework of quantile by reconstructing the gain coefficient and corrected procedure as the way used in the traditional Kalman filter model. The main superiority of our algorithm is that the proposed algorithm could adaptively adjust the existed prediction of risk based on the updated observations and forecast the next value of risk by using the adjusted result so that the accumulation of prediction bias of continuous forecasting process will be reduced dramatically and the precision of risk prediction will be promoted obviously. This superiority has been verified theoretically and empirically. Our theoretical analysis illustrates that the corrected result derived from the corrected procedure keeps unbiased and owns smaller variance compared with the input value of risk. If the prediction is implemented on the basis of the corrected result， it will decline the accumulation of error emerged in the whole process of forecasting， which theoretically uncovers the radical cause of the superiority of our algorithm. Moreover， the empirical conclusion shows the proposed algorithm owns better performance in the application and can realize more accurate risk-prediction comparing with the existing method. Furthermore， the superiority of our algorithm is more obvious in extreme situations. The construction of new algorithm not only enriches the means of risk forecasting， but also provides technical reference for avoiding risks suitably， especially for extreme risks.

Key words: VaR, kalman filtering, quantile regression, risk prediction