A thorough analysis of commercial banks' product innovation performance is essential to promoting bank product innovation capabilities and sustainable development. In this paper, the product innovation performance of commercial banks is defined as the conversion efficiency of input and output factors. The credit risk of product innovation of banks is considered as an undesirable output and incorporated in the performance evaluation system. Depending on whether there is a synchronous relationship between innovation income and risks, a Fixed Correlation model (FCM) and a Variable Correlation model (VCM) are then constructed based on Data Envelopment Analysis (DEA) method for the evaluation of commercial bank product innovation performance. In addition, an output optimization model of the objective function is also constructed to estimate the target income of commercial banks' product innovation in the FCM and VCM. Finally, the proposed model is applied to Chinese listed commercial banks for estimating the performance and target income of product innovation.Sustainability 2020, 12, 1523 2 of 15 Chinese commercial banks' product innovation, since it is a total factor efficiency evaluation method that can evaluate the efficiency of decision making units (DMU) with multiple inputs into multiple outputs [7]. As a non-parametric total factor productivity evaluation method, the DEA method can effectively avoid model misspecification. As such, it has been widely used in estimating total-factor efficiencies [8,9].Although banks can generate more revenue through innovative products [2], it is noted that different from other industries' innovation, financial product innovation also creates potential risks for bank operations. Calmès and Théoret [10], Aktan et al. [11] analyzed the statistics of commercial banks in Canada and Istanbul, respectively, and found that the growth of the innovative products may lead to an increase of risks for commercial banks. Therefore, it is of great significance to consider the impact of product innovation risks when analyzing the performance of commercial banks' product innovation. According to the Core Indicators for the Risk Management of Commercial Banks released by the China Banking Regulatory Commission, risks faced by commercial banks mainly include the liquidity risk, the credit risk, the market risk and the operational risk. Considering the reality of product innovation in Chinese commercial banks, it could be discovered that commission revenue related to loans and quasi-loans are the main source of banks' handling charge income [12], the credit risk can be seen as the major risk involved in the process of product innovation. As such, in this paper, the credit risk is considered as an undesirable output and is incorporated in the performance evaluation system.As a research on the evaluation of bank product innovation performance, the main contribution of this article lies in the fact that the FCM and VCM are constructed based on DEA for evaluating commercial banks' product innovation pe...