不确定理论下的股票抵押贷款的估值

Valuation of Stock Loan Under Uncertain Theory

基于不确定理论基础研究股票抵押贷款的估值问题,在假设股票价格符合不确定微分方程的基础上,得到了标准的股票抵押贷款价值函数的定价公式,分别推导出带有固定上限和固定增长率上限的股票抵押贷款价值函数的定价公式,运用数值算法计算不同情况下的股票抵押贷款价值以及贷款费用,最后研究了各相关参数与股票抵押贷款的价值函数之间的关系.结果表明贷款金额和贷款利率的增加会导致股票贷款价值减少,上限的增加和上限增长率的增加会导致股票贷款价值增加.

Under the framework of uncertainty theory, the valuation of stock loan was investigated. Based on the assumption that the underlying stock price follows an uncertain differential equation, the stock loan pricing formulas for uncertain stock model was obtained. The pricing formulas of stock loan value function with constant caps and caps with a constant growth rate were derived respectively. On this basis, the numerical algorithm was used to calculate the value of the stock mortgage loan and the loan expense under different circumstances. Finally, the relationship between the relevant parameters and the value function of the stock mortgage was studied. The results show that the increase of loan amount and loan interest rate will lead to the decrease of stock loan value, and the increase of the upper limit and the increase of the upper limit growth rate will lead to the increase of stock loan value.