Purpose The purpose of this paper is to develop a loan insurance pricing model allowing for the skewness and kurtosis existing in underlying asset returns. Design/methodology/approach Using the theory of Gram-Charlier option, the authors first derive a closed-form solution of the Gram-Charlier pricing model. To address the difficulties in implementing the pricing model, the authors subsequently propose an iterative method to estimate skewness and kurtosis in practical application, which shows a relatively fast convergence rate in the empirical test. Findings Not only the theoretical analysis but also the empirical evidence shows that the effects of skewness and kurtosis on loan insurance premium tend to be negative and positive, respectively. Furthermore, the actual values of skewness and kurtosis are usually negative and positive, respectively, which leads to the empirical result that the pricing model ignoring skewness and kurtosis substantially underestimates loan insurance premium. Originality/value This paper proposes a loan insurance pricing model considering the skewness and kurtosis of asset returns, in which the authors use the theory of Gram-Charlier option. More importantly, the authors further propose a novel iterative method to estimate skewness and kurtosis in practical application. The empirical evidence suggests that the Gram-Charlier pricing model captures the information content of skewness and kurtosis.

中文翻译：

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基于Gram-Charlier期权模型的贷款保险定价

目的本文的目的是开发一种贷款保险定价模型，以考虑基础资产收益中存在的偏斜和峰度。设计/方法/方法使用Gram-Charlier期权理论，作者首先得出了Gram-Charlier定价模型的封闭式解决方案。为了解决定价模型实施中的困难，作者随后提出了一种迭代方法来估计实际应用中的偏度和峰度，该方法在经验检验中显示出相对较快的收敛速度。结果不仅理论分析而且经验证据表明，偏度和峰度对贷款保险费的影响分别为负和正。此外，偏度和峰度的实际值通常分别为负和正，得出的经验结果是，忽略偏度和峰度的定价模型大大低估了贷款保险费。独创性/价值本文提出了一种考虑资产收益率偏度和峰度的贷款保险定价模型，在该模型中，作者使用了Gram-Charlier期权理论。更重要的是，作者进一步提出了一种新颖的迭代方法来估计实际应用中的偏斜度和峰度。经验证据表明，Gram-Charlier定价模型可以捕获偏度和峰度的信息内容。在其中作者使用了“ Gram-Charlier选项”理论。更重要的是，作者进一步提出了一种新颖的迭代方法来估计实际应用中的偏斜度和峰度。经验证据表明，Gram-Charlier定价模型可以捕获偏度和峰度的信息内容。在其中作者使用了“ Gram-Charlier选项”理论。更重要的是，作者进一步提出了一种新颖的迭代方法来估计实际应用中的偏斜度和峰度。经验证据表明，Gram-Charlier定价模型可以捕获偏度和峰度的信息内容。