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Pricing of Margin Call Stock Loan Based on the FMLS
Mathematical Problems in Engineering ( IF 1.430 ) Pub Date : 2020-06-27 , DOI: 10.1155/2020/5349345
Kaili Xiang 1 , Peng Hu 1, 2 , Xiao Li 1
Affiliation  

In common stock loan, lenders face the risk that their loans will not be repaid if the stock price falls below loan, which limits the issuance and circulation of stock loans. The empirical test suggests that the log-return series of stock price in the US market reject the normal distribution and admit instead a subclass of the asymmetric distribution. In this paper, we investigate the model of the margin call stock loan problem under the assumption that the return of stock follows the finite moment log-stable process (FMLS). In this case, the pricing model of the margin call stock loan can be described by a space-fractional partial differential equation with a time-varying free boundary condition. We transform the free boundary problem to a linear complementarity problem, and the fully-implicit finite difference method that we used is unconditionally stable in both the integer and fractional order. The numerical experiments are carried out to demonstrate differences of the margin call stock loan model under the FMLS and the standard normal distribution. Last, we analyze the impact of key parameters in our model on the margin call stock loan evaluation and give some reasonable explanation.

中文翻译:

基于FMLS的追加保证金贷款定价。

在普通股贷款中,如果股票价格低于贷款,贷方将面临无法偿还其贷款的风险,这限制了股票贷款的发行和流通。经验检验表明,美国市场上股票价格的对数回报系列拒绝了正态分布,而是接受了非对称分布的一个子类。在本文中,我们在保证金收益遵循有限矩对数稳定过程(FMLS)的假设下研究保证金催缴股票贷款问题的模型。在这种情况下,可以通过具有随时间变化的自由边界条件的空间分式偏微分方程来描述追加保证金股票贷款的定价模型。我们将自由边界问题转换为线性互补问题,并且我们使用的完全隐式有限差分方法在整数和分数阶上都是无条件稳定的。进行了数值实验,以证明在FMLS和标准正态分布下追加保证金的股票贷款模型的差异。最后,我们分析了模型中关键参数对追加保证金股票贷款评估的影响,并给出了一些合理的解释。
更新日期:2020-06-27
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