关键词: 损失分布, 资本配置, 存款保险, 鞍点法

Abstract: China officially implemented the deposit insurance system on May 1, 2015. The Deposit Insurance Regulations promulgated by the State Council stipulate that the deposit insurance rate consists of two components: The base rate and the risk differential rate. However, the rate system implemented at present does not yet truly reflect the differences in risk across banks, which means that the existing deposit insurance pricing methodologies still can't provide sufficient theoretical support for determining a reasonable risk-based rates.The pricing of deposit insurance is usually based on two paradigms: One approach is to price deposit insurance based on expected losses, which is limited to a small number of commercial banks with external credit ratings. Another approach is to use option theory to pricing deposit insurance, which is typically used for listed banks. However, the majority of the 3996 insured banks in China are unlisted small and medium-sized banks without external credit ratings. As a result, they cannot use either pricing method mentioned above to determine their deposit insurance rates. Therefore, the empirical study did not cover these small and medium-sized banks. This paper aims to establish a deposit insurance pricing methodology that better suits China's national conditions, helping to calculate premium for insured banks, especially numerous small and medium-sized banks. This will provide support for the top-level design of the deposit insurance premium rate system.
Firstly, this paper extends the pricing method of expected losses based on the relationship between bank loss distribution, capital allocation, and deposit insurance pricing. The paper provides a pricing formula for deposit insurance that takes into account these factors. Based on this, the paper proposes a new method of measuring deposit insurance premium based on the loss distribution of bank's unit asset, defined by dividing the loss distribution of the entire bank's assets by its current total amount. This significantly reduces the cost of measuring deposit insurance premiums by requiring only a statistical sample of some of the bank's assets rather than measuring the loss distribution for every asset loss. Secondly, this paper treats the bank assets obtained through sampling as a loan portfolio. With reference to the Creditrisk+model, which is a well-known approach to modeling credit risk, the paper constructs the loss distribution of the loan portfolio and solves its loss distribution using the saddle point method. In doing so, the paper accounts for the loss given default of the loan portfolio, resulting in a more accurate measurement of the loss distribution of unit asset compared to the Creditrisk+ model. The methodology enriches the deposit insurance pricing by incorporating research outcomes from the field of credit risk modeling.
The case study shows that: (1)The deposit insurance premium is significantly affected by the loss given default of commercial banks' assets, implying that improving the quality of commercial banks' assets is crucial to reducing the deposit insurance rate. (2)The data used in this article's method are readily available. The data of banks' assets, liabilities, and risk capital are all required to be publicly disclosed by regulation. The National Administration of Financial Regulation (NAFR) usually requires commercial banks to provide data for risk measurement and simulation of the loan portfolio, so sample data for the loan portfolio can be obtained from the supervisory authority. (3)The method does not depend on external rating data and market price data of bank stocks, and is applicable to all banks, so it has broad application prospects.

Key words: loss distribution, capital allocation, deposit insurance, saddle point