递阶双因素模型估计信用组合一致性风险

Estimating the Coherent Risk Measure of Credit Portfolio Based on Hierarchical Two-factor Model

当信用组合内资产个数较少时,基于Gordy提出的粒度调节方法计算的组合风险量度VaR将严重被低估,从而高估一致性风险量度预期短缺ES。本文利用Taylor展开式改进粒度调节方法,提高估计ES的准确性;并且假设行业因素是宏观经济因素的线性函数,由此保证了组合不变性的条件,从而扩展单因素模型为递阶双因素模型,提高相关性估计准确性,解决了单因素模型高估经济资本的问题。模拟结果显示递阶双因素模型的优越性,特别是组合内资产规模较小时,改进的效果更明显。

As the number of assets in credit portfolio becomes comparatively small, the risk measure VaR calculated by the granularity adjustment approach, introduced by Gordy, will be seriously underestimated. Consequently coherent risk measure （Expected Shortfall） will be overestimated. In this paper, the estimation of ES is improved by granularity adjustment approach through Taylor expansion. On the assumption that industry factor is the linear function of macro-economic factor, so the portfolio invariance condition will be maintained, and it is practicable to develop single factor model into double factor model, which improves the estimation of correlation and solves the problem of overestimating capital charges in single factor model. The results of simulation present the advantages of double factor model. Especially the smaller the asset scale is, the more effective it is.