The purpose of this paper is to develop a loan insurance pricing model allowing for the skewness and kurtosis existing in underlying asset returns.
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.
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.
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.
The authors are grateful to the editor and anonymous referees for their insightful comments that help to improve the quality of this paper. This work is supported by the National Natural Science Foundation of China (71371157, 71671145), the humanities and social science fund of Ministry of Education (15YJA790031, 16YJA790062, 17YJA790015, 17XJA790002), and the young scholar fund of Science & Technology Department of Sichuan province (2015JQO010). In particular, Yaojie Zhang acknowledges the support from Doctoral Innovation Fund Program of Southwest Jiaotong University (D-CX201724) and Service Science and Innovation Key Laboratory of Sichuan Province (KL1704).
Zhang, Y., Wei, Y. and Shi, B. (2018), "The pricing of loan insurance based on the Gram-Charlier option model", China Finance Review International, Vol. 8 No. 4, pp. 425-440. https://doi.org/10.1108/CFRI-10-2017-0210
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