Research On Pricing Of Multi-maturity Deposit Insurance Based On Knight Uncertainty

Along with the steady development of financial liberalization and interest rate risk,the commercial bank’s debt management pattern is prone to risk and instability.Therefore,how to prevent commercial bank operational risks and prevent bank risks from leading to crises in the entire banking industry is a key issue that the banking industry needs to face.Currently,there is a growing number of countries implementing explicit deposit insurance systems,and all countries have realized that the deposit insurance system is a feasible option to regulate and standardize the banking industry.However,there are still problems of moral hazard and adverse selection in the development of deposit insurance,and the reason for these problems lies in the unreasonable setting of deposit insurance rates.Thus,in order to protect bank assets,a reasonable measurement of the risk of bank assets and thus a scientific determination of deposit insurance rates has become the key to the effective implementation of a deposit insurance system.When measuring the asset risk of commercial banks,traditional models mostly consider one-sidedness.Generally,it is assumed that commercial banks have sufficient rationality when investing in the financial market,can foresee all uncertain states in the financial market,and estimate the probability of uncertainty.However,in the rapidly changing financial market,the investment rationality of commercial banks is limited.In addition,the risk in the traditional model cannot explain the "smile volatility" and other abnormal phenomena in the financial market,but Knight uncertainty can give a good explanation.Therefore,Knight uncertainty is a risk factor that cannot be ignored in the study of deposit insurance pricing.The premise of deposit insurance pricing is that the market is efficient,and Knight uncertainty is also obtained in the securities market.Therefore,before building the model,the paper selects the S&P 500 index market data as the overall situation reflecting the effectiveness of commercial banks’ investment in the securities market.Through empirical analysis,it is concluded that the securities market is an effective market.In addition,the paper uses one-minute high-frequency data on the S&P 500 to calculate Knight uncertainty and conduct a t-test on it,confirming that Knight uncertainty is non-negligible in the securities market.Knight uncertainty in the market cannot be ignored in asset pricing(Chen and Epstein,2002).In order to simplify the analysis,this paper only assumes that there is Knight uncertainty in the regulator’s assessment of owner’s equity only,and that Knight uncertainty also originates from the securities market.In this paper,we start from domestic and international multi-period deposit insurance pricing theories,select a suitable model to embed the risk of Knight uncertainty,and construct a multi-period deposit insurance pricing model using the Merton option pricing model.Given the commercial bank’s balance sheet,the bank’s optimal investment strategy is derived using the stochastic optimal control method in order to maximize the expected utility of the owner’s private equity holdings of the commercial bank subject to Knight uncertainty.Combined with asset replacement rules and dynamic optimization methods,a multi-period deposit insurance pricing model is derived based on HJB equation.The research results of this paper are obtained through the analysis of numerical examples.First,with the increase of Knight’s uncertainty,the deposit insurance rates levied by deposit insurance institutions will increase.Second,it is found that with the longer audit time span of deposit insurance institutions,the more obvious the impact of Knight uncertainty on deposit insurance rates.Third,the greater the ratio of initial deposit to assets,the more obvious the impact of Knight uncertainty on deposit insurance rates.The significance of this paper is to provide a comprehensive study of the multi-period deposit insurance pricing model and to revise the model with Knight uncertainty as a risk factor.According to the model,calculate the multi-period deposit premium under Knight uncertainty,and observe the impact of Knight uncertainty on deposit insurance premium.Finally,the paper advances policy recommendations for the deposit insurance system based on the results of the above analysis.