| This article, based on loan-to-value ratio as the research object, taking the method of model building, builds the loan-to-value ratio model under the different modes of pledge, and makes an important reference for the bank handling inventory financing business to small and medium-sized enterprises and deciding the optimal loan-to-value ratio, which is of important practical and theoretical significance. The innovation of the article, conducts sensitivity analysis on the optimal loan-to-value ratio and the maximum expected profit on study of inventory of the loan-to-value ratio model in the static pledge mode firstly, assumes that banks are setting an optimal loan-to-value ratio at every time to cover short positions to maximize expected profit of every stage on study of inventory of the loan-to-value ratio model in the dynamic pledge mode secondly, and considers banks of restriction of down-risk on study of inventory portfolio of the loan-to-value ratio model thirdly. Studies based on the static pledge mode on inventory of the loan-to-value ratio model have shown that, the relationships between the optimal loan-to-value ratio and not only the logarithm yields but also the logarithmic volatility are positively correlated, and the relationships between the optimal loan-to-value ratio and not only the loan interest rate but also the loan period and the probability of default are negatively correlated firstly, the relationships between the maximum expected profit and not only the logarithm yields but also the loan interest rate and the loan period are positively correlated, and the relationship between the maximum expected profit and the logarithmic volatility is negatively correlated, and the relationship between the maximum expected profit and the probability of default is complex, that is, with the increase of the probability of default, the maximum expected profit decreases and then increases and then decreases again secondly, the sensitivity of the optimal loan-to-value ratio about logarithmic volatility is the largest, followed by the logarithm yields, the loan interest rate, the loan period and the probability of default thirdly, the sensitivity of the maximum expected profit about the loan interest rate is the largest, followed by the logarithmic volatility, the loan period, the logarithm yields and the probability of default fourth. Studies based on the dynamic pledge mode on inventory of the loan-to-value ratio model have shown that, compared with the static pledge mode with the same loan period, at every time to cover short positions, banks can tolerate a large price drop of the inventory, get a high profit, and only require a low price of the inventory to achieve break-even point firstly, with increasing frequency of covering short positions, banks can tolerate larger price drop of the inventory, get higher profit, and only require lower price of the inventory to achieve break-even point secondly. Studies on inventory portfolio of the loan-to-value ratio model have shown that, the optimal loan-to-value ratio which makes banks achieve the maximum expected profit, either makes the banks’ expected profit function partial derivatives on the loan-to-value ratio zero, or just meets boundary conditions of restriction of down-risk, and if the optimal loan-to-value ratio meets the latter, the optimal loan-to-value ratio is the maximum loan-to-value ratio which the banks can provide, and the relationships between the maximum loan-to-value ratio and not only the amount of loan losses but also the risk tolerance levels are positively correlated, and the relationships between the maximum loan-to-value ratio and not only the loan interest rate but also the loan period and the probability of default are negatively correlated. |
