主 题：How Robust is the VaR of Credit Risk Portfolios ?
主讲人：姚经
主持人：龚金国
时 间：2014年7月2日上午10：30
地 点：通博楼B212学术会议室
主办单位：统计学院 科研处
主讲人简介：
姚经于2013年5月在布鲁塞尔自由大学获得了应用经济学博士学位，目前在布鲁塞尔自由大学做博士后研究。他的主要研究方向是概率论及统计在金融保险中应用；包括风险管理，衍生品定价，投资组合，渐进理论等方面。在The North American Actuarial Journal （北美精算）, Journal of Statistical Planning and Inference, ASTIN Bulletin 等期刊发表多篇论文。
内容提要：
In this paper, we assess the magnitude of model uncertainty of credit risk portfolio models, i.e., what is the maximum or minimum Value-at-Risk (VaR) that can be justified given a certain set of information? In the unconstrained homogeneous case, i.e., when the default probabilities, exposures and recovery rates of the different loans are known (and equal) but not their interdependence, some explicit sharp bounds are available in the literature. However, the problem is fairly more complicated when the portfolio is heterogeneous. In this regard, Puccetti and Rüschendorf (2012) and Embrechts et al. (2013) propose the rearrangement algorithm (RA) to approximate the unconstrained VaR bounds of a portfolio that can be heterogeneous. While their numerical examples provide evidence that the RA makes it indeed possible to approximate the sharp bounds accurately, their results also indicate that the gap between worst-case and best-case VaR numbers is typically very high. Hence, sharpening the VaR bounds by considering the presence of dependence information is of great practical relevance, but also hard to do because lack of sufficiently rich default data implies that knowledge of the joint default probabilities is typically not in reach. By contrast, the variance and perhaps also the skewness of the aggregated portfolio can be estimated statistically and can potentially be used as a source of dependence information allowing getting improvements of the VaR bounds.
We propose an efficient algorithm to approximate sharp VaR bounds in the unconstrained case, i.e., in comparison with the earlier algorithms that appeared in the literature, the algorithm that we propose is guaranteed to always converges to a candidate solution. Furthermore, we are able to adapt the algorithm so that it can deal with higher order constraints (variance, skewness, kurtosis,...). A feature of our approach is that we are able to incorporate statistical uncertainty on the moment constraints. We apply the results to real world credit risk portfolios and we show that in all typical situations VaR assessments that are performed at high confidence levels (as in Solvency II and Basel III) are not robust and subject to significant model uncertainty.
