Recovery Process Model
Recovery Process Model
复制标题
恢复过程模型
DOI：
10.1007/s10690-009-9083-7
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发表时间：
2008
影响因子：
1.7
通讯作者：
Yuki Itoh
中科院分区：
文献类型：
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作者：
Yuki Itoh
近年来，由于巴塞尔协议和次贷危机的影响，违约公司债务的回收规模和回收率的量化成为金融机构及其监管者面临的一个重要问题，但对于回收过程的结构，即回收规模与时间的关系，还没有研究。主动恢复模型在实现恢复之前不考虑恢复进度。我们直接为单个违约公司的债务恢复过程建模。我们用齐次复合泊松过程来模拟恢复过程，并将我们的模型扩展到非齐次复合泊松过程。在我们的模型中，利率是明确使用的。通过该模型，可以分析累积回收率、回收增量、初始负债额、最后回收可能时间与利率之间的关系。我们推导出了债务的生存值和回收率的期望值和方差，也推导出了回收完成时间的概率分布函数和期望值。此外，我们提出了基于Panjer递推公式和快速傅立叶变换的期望值和方差的数值计算方法，并给出了数值结果。本文还提出了一种计算非齐次复合Poisson过程转移密度的新方法。我们的方法是基于近似的非齐次复合泊松过程的分段齐次复合泊松过程。该方法用于计算非齐次复合Poisson过程的期望值和方差。
Recently, because of Basel II and the subprime mortgage crisis, the quantification of the recovery size and the recovery rate for the debt of a defaulted company is a serious problem for financial institutions and their supervisors, but there has been no study of structure of the recovery process which is the relationship between time and the cumulative recovery size. Existent recovery models do not regard the recovery progress before the time of achievement of recovery. We directly model recovery process for the debt of a single defaulted company. We model the recovery process by a homogeneous compound Poisson process and extend our model to an inhomogeneous compound Poisson process. The interest rate is explicitly used in our model. By our model, the relationship between the cumulative recovery, the increment of recovery, the initial debt amount, the last recovery possible time and the interest rate can be analyzed. We derive the expected value and the variance of the survival value of the debt and the recovery rate, and also derive the probability distribution function and the expected value of the recovery completion time. Moreover we present the numerical methods for calculating the expected value and the variance based on Panjer recursion formula and the fast Fourier transformation, and show numerical results. Also we propose a new method of calculating the transition density of an inhomogeneous compound Poisson process. Our method is based on approximating an inhomogeneous compound Poisson process by a piecewise homogeneous compound Poisson process. This method is used to compute the expected value and the variance of an inhomogeneous compound Poisson process.