We propose a new parsimonious model for valuating portfolio credit derivatives dependent on aggregate loss. The starting point is the loss distribution, which is constructed to be time dependent. We let the loss be beta distributed, and, by implication, the loss process becomes a stochastic jump process, where a jump corresponds to losses appearing simultaneously. The model matches empirical loss data well with only two parameters in addition to expected loss. The size of the jump is controlled by the clustering parameter, and the temporal correlation of jumps is controlled by the autocorrelation parameter. The full model is relatively efficient to implement, as we use a Monte Carlo at portfolio level. We derive analytical expressions for valuating tranches and for calculating regulatory capital. We provide examples of credit default swap index tranche pricing, including forward starting tranches. Comparisons are made with the one-factor Gaussian copula default time model, which fits historical loss data badly and has a deficient loss volatility term structure.

中文翻译：

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一个有效的投资组合损失模型

我们提出了一种新的简约模型，用于评估依赖于总损失的投资组合信用衍生品。起点是损失分布，它被构造为与时间相关的。我们让损失是 beta 分布的，并且，通过暗示，损失过程变成了随机跳跃过程，其中跳跃对应于同时出现的损失。除了预期损失外，该模型仅使用两个参数很好地匹配了经验损失数据。跳跃的大小由聚类参数控制，跳跃的时间相关性由自相关参数控制。完整的模型实施起来相对有效，因为我们在投资组合级别使用蒙特卡洛。我们推导出用于评估批次和计算监管资本的分析表达式。我们提供了信用违约掉期指数部分定价的示例，包括远期起始部分。与单因素高斯copula默认时间模型进行比较，该模型与历史损失数据拟合度差，损失波动率期限结构不足。