In the credit risk weighted assets formula for derivatives, the exposure-at-default is scaled by a multiplier: the so-called internal alpha factor. This has been introduced by the Basel Committee to offset the model or estimation error arising from the usage of a constant exposure amount and should account for the uncertainty of counterparty exposure, the correlation between exposures and the correlation between exposure and default. In this paper, we investigate the alpha factor’s sensitivity to key model parameters under stylized portfolio assumptions in order to better understand its complex characteristics. Our analysis is based on the numerical simulation of alpha sensitivities as well as the derivation of analytical formulas under the assumption of infinitely granular portfolios. We show that the relative exposure volatility and parameters that specify the link between the underlying credit portfolio model and the exposure variables (wrong-way/right-way risk parameters) have a particularly significant impact on the alpha factor. For small homogeneous portfolios the alpha factor is rather unstable with respect to the number of counterparties. We investigate an alternative definition based on the coherent risk measure expected shortfall, which reduces the alpha instability quite significantly.


中文翻译：

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α因子的敏感性分析

在衍生品的信用风险加权资产公式中，违约风险敞口由一个乘数衡量：所谓的内部阿尔法因子。巴塞尔委员会已引入此项以抵消因使用恒定风险金额而产生的模型或估计误差，并应考虑交易对手风险的不确定性、风险之间的相关性以及风险与违约之间的相关性。在本文中，我们研究了在程式化投资组合假设下阿尔法因子对关键模型参数的敏感性，以便更好地理解其复杂特征。我们的分析基于对 alpha 敏感性的数值模拟以及在无限粒度投资组合假设下推导分析公式。我们表明，相对暴露波动性和指定基础信贷组合模型与暴露变量（错误方向/正确方向风险参数）之间联系的参数对 alpha 因子具有特别显着的影响。对于小型同质投资组合，alpha 因子相对于交易对手的数量相当不稳定。我们研究了一个基于连贯风险度量预期不足的替代定义，它显着降低了 alpha 不稳定性。