Non-tradable shares pricing and optimal default point based on hybrid KMV models: Evidence from China

Aiming to improve the KMV model as well as estimate the price discount on non-tradable shares, this paper proposes the methods of particle swarm optimization and maximum likelihood estimation to develop the PSO-KMV model. We find evidence that the PSO-KMV model significantly outperforms the KMV model and the market price of non-tradable shares estimated by the PSO-KMV model is reasonable. Besides, particle swarm optimization is more suitable than genetic algorithm in this study. Further, the method of fuzzy clustering is applied to the PSO-KMV model. Then the FC-PSO-KMV model obtains a more specific default point composed of four parts of liabilities instead of short-term debt and long-term debt, and thus performs slightly better than the PSO-KMV model. The empirical results demonstrate that the short-term debt of China, especially the short-term loan, is far riskier than that of the U.S. In summary, the hybrid KMV models provide more accurate predictions so as to effectively assess and manage credit risk.