Abstract: In recent years, China's economy has entered a new normal and financial reforms have continued to deepen. Therefore, commercial banks have intensified their innovation and various types of innovative products have emerged rapidly. As a result, analyzing the product innovation performance of commercial banks is particularly important for promoting the development of commercial banks and enhancing the competitiveness of commercial banks. Considering the risks in the process of commercial bank product innovation, an improved data envelopment analysis (DEA) framework is proposed to evaluate the performance of bank product innovation. Credit risk in the process of commercial bank product innovation is considered as an undesired output and incorporated into the evaluation index. According to whether there is a synchronous relationship between innovation income and credit risk, undesirable outputs are set with strong disposability and weak disposability respectively. Then, the fixed correlation model (FCM) and the change correlation model (VCM) based on DEA are constructed and used for commercial bank product innovation performance evaluation. Subsequently, by constructing the output optimization model of the objective function, the target revenue of product innovation under the FCM and VCM models is estimated. By decomposing the added value of target income under the two models, the promotion of product innovation income of commercial banks is decomposed into technical and non-technical reasons. The decomposition of added value is also used as the basis for analyzing the level of risk management. Finally, the proposed DEA framework is applied to 25 Chinese listed commercial banks based on the data in the year of 2013, 2015 and 2017. Through the analysis of product innovation performance, the conclusions are as follows:(1) In 2013-2017, the product innovation gaps of the four types of commercial banks were large, the performance of joint-stock banks was at the highest level, and the efficiency of rural commercial banks was the lowest. During the period of observation, the efficiency of joint-stock banks and city commercial banks showed an upward trend, and the change in the efficiency value of state-owned banks was reversed. (2) Under the constraints of existing risk management levels, joint-stock banks and city commercial banks need to reduce the scale of product innovation and reduce corresponding income. After improving the level of risk management, the commercial innovation income of commercial banks will be effectively improved. (3) Through the optimization of risk management technology, the rural commercial bank's product innovation income has the largest proportion of changes, followed by city commercial banks, joint-stock banks and state-owned banks. The change ratio also reflects the current level of risk management of commercial banks. From the perspective of absolute income changes, state-owned banks have the greatest gains through risk management. According to the research conclusions, several management suggestions are also proposed for commercial banks to promote their product innovation performance and strengthen their risk management capabilities.

Key words: data envelopment analysis, commercial bank product innovation, performance evaluation, innovation risk