The Application Of Forward And Backward Stochastic Differential Equations In Deposit Insurance Pricing

China places a high priority on preventing and controlling financial risks due to the continuous development of economic situation and financial system.Banks are still the leading role in China’s financial activities despite the development of financial system tends to be diversified,and the stability of the banking sector is related to the security of the whole financial business.The proposed deposit insurance system can protect the vital interests of depositors and promote fair competition among banks,which is critical to maintain market stability and to ensure the sustainable and healthy development of our economy.Currently,China implements the deposit insurance system in which benchmark rates and risk differential rates coexist.The key to the successful implementation of this system lies in the reasonable determination of the deposit insurance preminum rates.In 1977,Merton considered deposit insurance as a put option purchased by a bank from the deposit insurance institution and constructed an option pricing model for deposit insurance.Backward Stochastic Differential Equation(BSDE)has been successfully applied to option pricing problems,and the research on numerical solutions of Forward and Backward Stochastic Differential Equations(FBSDEs)has been relatively mature.In this thesis,we apply FBSDEs to the field of deposit insurance pricing and use the numerical scheme of FBSDEs to empirically study the deposit insurance premium rates of listed banks in China.The main contents and innovations are as follows:1.We present FBSDEs for the European call option price when the stock price obeys a general stochastic process in the two cases of discontinuous dividend payment and continuous dividend payment.At the same time,the drift coefficient and generator in FBSDEs are transformed by nonlinear Feynman-Kac formula to obtain the simpler FBSDEs.Under continuous dividend payment,numerical experiments are carried out with the FBSDEs satisfied by the price of the European call option.2.We introduce regulatory forbearance,continuous dividend payment,bank liability structure and liquidation costs into deposit insurance pricing model.Then we derive FBSDEs for deposit insurance premiums by varying the generator and terminal conditions.We correct the compensation amount of deposit insurance institution under the regulatory forbearance system.Liquidation costs are innovatively introduced under the conditions of regulatory forbearance and continuous dividend payment.Considering the four factors when determining deposit insurance premium rates more realistic.3.In empirical analysis,a total of 19 listed banks in four categories in China are selected for study.The maximum likelihood estimation method is used to estimate the parameters in the model.The generalized θ-scheme is used to solve the FBSDEs satisfied by the deposit insurance premiums for each bank under different factors,which leads to the deposit insurance premium rates.The numerical results show that considering the regulatory forbearance system will reduce the deposit insurance premium rates,and the higher the dividend rates and liquidation costs,the higher the deposit insurance premium rates.Considering the bank debt structure will not affect the size of the deposit insurance premium rates.The results are consistent with the actual situation,which verifies the feasibility of solving deposit insurance pricing model by FBSDEs.We also find that there is a significant stratification phenomenon of deposit insurance premium rates in the four types of banks.The state-owned banks have significantly lower deposit insurance premium rates compared with other types of banks.This further confirms the necessity of implementing risk differential premium rates in China.