模糊厌恶下关系型借贷定价和最优贷款利率

考虑决策者是模糊厌恶的，利用实物期权方法，解析地给出了银行价值，企业价值和最优停贷水平。分析了模糊厌恶和基准波动率对最优贷款利率，最优停贷水平，企业价值和银行价值的影响。数值分析表明：模糊厌恶提高了贷款利率，降低了企业和银行价值。在基准波动率水平较小时，模糊厌恶推迟了停贷水平；在基准波动率较大时，模糊厌恶加速了停贷水平。此外，在模糊中性下，企业价值是基准波动率凸函数，银行价值是基准波动率凹函数。而在模糊厌恶下，企业价值和银行价值都随着基准波动率的增加而递减。本文从行为金融角度为中小企业"融资贵"提供了新的解释。

The Pricing of Relationship Loan and Optimal Loan Interest Rate under Ambiguity Aversion

Under the new normal of the economy, the difficult financing for small and medium-sized enterprises (SMEs) is a prominent problems. The reason of the difficult financing for SMEs is that there exists information asymmetry between bank and SMEs. Stiglitz and Weiss (1981) deemed that information asymmetry causes adverse selection and moral hazard problems, and strengthen the credit rationing of bank. Thus, it makes SMEs's financing difficult and increases the cost of financing. However, the relationship loan is a important way to resolve the information asymmetry between bank and SMEs. Thus, it is significant to alleviate the financing constraint for SMEs. DeYoung et al.(2008), Bharath et al.(2009) and Beck et al.(2018) found that the relationship loan promotes information communication between bank and SMEs via multi-channel, long-term contact SMEs. It lowers the condition of financing for SMEs by making full use of SMEs' soft information. According to the data from the National bureau of statistics, it shows that 38.8 percent of SMEs with need financing can not gain the fund. The phenomenon of the stint loans and broken credit of bank happens all the time. Furthermore, the bank increases the 30 percent of interest rate for SMEs. From the above, it shows that the phenomenon of financing expensive for SMEs is common. Based on this, our model incorporates decision-makers' ambiguity aversion to study the relationship loan, and provides behavioral explanation for the phenomenon of financing expensive for SMEs.Following Agliardi et al.(2015), it is assumed that the cash flow X satisfies the Choquet-Brownian process:dX_t=(μ+mσ)X_tdt+sσX_tdZ_twhere μ+mσ denotes the growth rate of cash flow, and sσ denotes the volatility of cash flow, and μ、σ are constant. m=2c-1, s²=4c(1-c), where c∈(0,1) is constant and measures the degree of the decision-makers' ambiguity about the future results. In our model, we focus on the ambiguity aversion case, i.e., c<1/2. The smaller the value of c is, the more ambiguity aversion the decision-makers are.Following Zhang and Huang(2016), it is assumed that there exists a relationship loan between bank and SMEs. In this contract, bank gain the portion θ of cash flow by pay cost f. Let x_l denote the credit crunch threshold, which is determined by maximizing the value of bank. When bank stop providing loan for SMEs, the agents (bank and SMEs) gain nothing.According to the real-options approach, bank value, firm value and optimal credit crunch threshold are explicitly deriued. The impacts of the ambiguity aversion and baseline volatility on optimal loan interest rate, optimal credit crunch threshold, firm value and bank value are examined. By numerical analysis, it is discovered that ambiguity aversion increases loan interest rate, and the firm value and bank value are reduced. Ambiguity aversion delays credit crunch threshold for the low level of baseline volatility and accelerates credit crunch threshold for the high level of baseline volatility. What's more, it is found that under ambiguity neutral, firm value is a convex function of baseline volatility and bank firm is a concave function of baseline volatility. Under ambiguity aversion case, firm value and bank value decrease with baseline volatility. A behavioral explanation is provide for the high financing cost of SMEs.