Abstract: The existing loan insurance pricing models commonly ignore the impact of default threshold and early default on loan losses. Based on the down-and-in put option, which is one kind of barrier options, this paper introduces the two key factors into the new pricing model of loan insurance. Furthermore, this study provides the estimation of knock-in probability and knock-in time of loan insurance by Monte Carlo simulation. In addition, this paper applies the new loan insurance pricing model to the practice by the method of KMV model and makes an empirical analysis. The results show that an increase in default threshold would lead to an increase in loan insurance premium and knock-in probability, and also results in an earlier knock-in time. Therefore, the accurate estimate of default threshold is of critical importance for our model. Furthermore, a higher observation frequency of corporate defaults would result in a higher loan insurance premium. In other words, that banks reduce the observation frequency of corporate defaults would lead to the loss of loan insurance.

Key words: loan insurance, barrier option, down-and-in put option, default threshold, knock-in time

摘要： 现有的贷款保险定价模型通常忽略了违约门槛和提前违约对贷款损失的影响。本文基于障碍期权中的向下敲入看跌期权,将这两个重要因素纳入到了新的贷款保险定价模型中。进一步,本文通过蒙特卡洛模拟的方法,给出了贷款保险敲入概率和敲入时间点的估计过程。此外,本文将新构建的贷款保险定价模型应用于实际中,并进行了实证分析。结果表明,违约门槛的上升会提高贷款保险的定价水平和敲入概率,并导致更早的敲入时间点。而银行降低对企业违约情况的观察频率会引起贷款保险的价值损失。

关键词: 贷款保险, 障碍期权, 向下敲入看跌期权, 违约门槛, 敲入时间点