Endogenous Quantile Level In VaR Modeling

In VaR modeling, the confidence level is set exogenously in requirement of BaselCommittee's regulation for risk monitoring and management. However, because of thenon-normality distribution of the financial data, the coefficients estimate,the goodness offit and the effectiveness of prediction of many VaR models are rather sensitive to thechoice of confidence level per se. Thus, as many researches have shown, theout-of-sample prediction ability of the models varies dramatically from that of in-sample.The CAViaR model, Conditional Autoregressive Value-at-Risk, introduced by Engle andManganelli(1999) is a typical example of the argument. Therefore, we propose toinvestigate the choice of confidence level basing on the inner factors of the models andconsider setting the quantile level endogenously. This paper aims to measure and improve VaR models' stability of prediction. Whenmodeling a time series whose data generating process (DGP) is coherent, we can say thatthe prediction ability of the model is stable if the out-of-sample prediction is within thegiven domain. On one hand, we consider the requirement that the hit series (ordeparture-indicator series) is i.i.d (independent identical distribution). Basing on the ideaof backtesting, we expanded the application of DQ (dynamic quantile) test proposed byEngle and Manganelli(1999), and through a serial of Mont Carlo simulation we testifiedthat many models' DQ values are very flexible to confidence level. We pick out the stableregions where theDQθ values are consecutively significant. These regions are taken asoptimal for the model and the model can be regarded as effective if θ is chosen fromthem. One the other hand, to evaluate models' prediction precision, we devise theindirect-adequacy-of-fit statistics (IAF) to measure their prediction efficiency andlikelihood ratio test based on the minimized weighted-absolute-average-error (WAAE) to IIIevaluate the variation of prediction efficiency. Similarly, we used Mont Carlo simulationto test the properties of these two statistics. With above three statistics we cansystematically survey the movement of the prediction efficiency in an interested domainof the confidence level so as to set an optimal one for risk management process. Empirical analysis on the returns of Shanghai Exchange Index and many stockswere also used to testify the effectiveness of the endogenous confidence level methodsproposed in this paper and confirm its necessity in risk management practice. What's new do we disclose in this paper? Firstly, exogenous confidence level inVaR model is proposed, and this proposal is supported by simulation and empiricalanalysis from the perspective of model's prediction precision and stability of predictionability, and a suit of endogenous confidence level method is preliminarily established. Anatural inference of this research is, a corresponding variation is apt to occur to VaRmodel's prediction ability in according to the domain of quantile selected. Accordingly,this paper testified that, to use the departure-indicator proposed by Basel Committee onbanking supervision (1996) to compare VaR models' prediction efficiency may incurfallacy whose mode is related to the property of given model and data, and that thisdeparture-indicator is generally ineffective and biased when significance level is under2% . Secondly, we proposed the indirect-adequacy-of-fit statistics to fill the gap ofgoodness-of-fit in quantile regression, and its rationality and effectiveness is to bestudied and testified further.