Whilst there is increasing research attention on predicting financial distress, the existing literature is subject to two specific limitations. The first is that a firm can experience a financial distress event (e.g., loan default, bankruptcy) more than once, yet most studies that model corporate financial distress prediction treat financial distress as occurring only once. This approach leads to an inefficient use of data with all subsequent events being ignored and subsequently a decrease in statistical power. Second, to account for the lack of independence between observations of repeated event data, the extant research utilising hazard analysis either has a separate analysis for successive distressed events or relies upon robust standard errors. In addition to a much smaller sample, a separate analysis yields the models that can be used to predict the survival of a distressed firm rather than the survival of a firm generally. The method of robust standard errors, while innocuous to one-time event data, ignores the possible downward bias in coefficient estimates for repeated event data. To address these two limitations, we treat financial distress as repeated events and apply more advanced methods (generalised estimating equations, random effects, fixed effects, and a hybrid approach) to account for the lack of independence between observations in discrete time hazard analysis. These different approaches are applied to a sample of listed companies in China over the 2007‒2021 period. We find that variables that are not statistically significant in models based on one-time events data become statistically significant in the models based on repeated events data, and that coefficient estimates are larger in their magnitude with more advanced methods than with the method of robust standard errors. We also find that among the advanced methods, a hybrid approach achieves substantially better out-of-sample prediction, particularly over a long-term horizon than other approaches. Our results remain robust in tests of robustness.

ABSTRACT：As an important derivative instrument, CDO is playing a crucial role in the financial crisis. With complicated structure, we have developed many pricing models, which all relay on complicated mathematical model. The paper, firstly, introduces the mainstream pricing model----structural model and reduced form model. Then we introduced the Hybrid Models based on two formal models, by discussing the parameter of pricing i.e. default probability, default free risk and default correlation. In this paper, we give the hybrid model by Monte Carlo simulation based on copula function. Finally, we consider the pricing sensitivity on various parameters. According to the result of simulation, the relationship between the tranches price and pricing parameters is various. For the equity tranche and mezzanine tranche, the price and recovery rate have a positive correlation, while the case is inverse for the senior tranche. We also can conclude that, higher default correlation can lower the price of equity tranche, and have an opposite effect on the senior tranche. The influence on the mezzanine tranche isn’t certain. Furthermore, by comparing two different copula function model, we can get that marginal distribution has different effect on the tranches price.