论文标题
使用默顿模型和相变的参数估计默认投资组合
Parameter estimation of default portfolios using the Merton model and Phase transition
论文作者
论文摘要
我们讨论默认概率（PD），债务人之间的相关性和相变的参数估计。在以前的工作中，我们使用β-二项式分布研究了问题。当幂律的时间相关性衰减时，具有顺序参数的非平衡相变。在本文中，我们采用了默顿模型，该模型将资产相关性用作默认相关性，并发现当幂律的时间相关性衰减时发生相变。当功率指数小于1时，PD估计器会收敛缓慢。因此，很难用有限的历史数据来估计PD。相反，当功率指数大于一个时，收敛速度与样品数量成反比。我们研究了几个评级机构的经验默认数据历史记录。当我们使用较长的历史记录数据时，估计的功率指数在缓慢的收敛范围内。这表明PD可能具有较长的内存，并且由于收敛速度缓慢而难以估计参数。
We discuss the parameter estimation of the probability of default (PD), the correlation between the obligors, and a phase transition. In our previous work, we studied the problem using the beta-binomial distribution. A non-equilibrium phase transition with an order parameter occurs when the temporal correlation decays by power law. In this article, we adopt the Merton model, which uses an asset correlation as the default correlation, and find that a phase transition occurs when the temporal correlation decays by power law. When the power index is less than one, the PD estimator converges slowly. Thus, it is difficult to estimate PD with limited historical data. Conversely, when the power index is greater than one, the convergence speed is inversely proportional to the number of samples. We investigate the empirical default data history of several rating agencies. The estimated power index is in the slow convergence range when we use long history data. This suggests that PD could have a long memory and that it is difficult to estimate parameters due to slow convergence.
