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Estimation of Default Probability by Structural Model
Stationary-leverage-ratio models of modelling credit risk based on constant target leverage ratios cannot generate probabilities of default which replicate empirically observed default rates. This paper presents a structural model to address this problem. The main feature of the model is that a firm’s leverage ratio is mean-reverting to a time-dependent target leverage ratio. The time-dependent target leverage ratio reflects the firm’s intention of moving its initial target ratio toward a long-term target ratio over time. We derive a closed-form solution of the probability of default based on the model as a function of the firm value, liability and short term interest rate. The numerical results calculated from the solution with simple time-dependent functions of the target leverage ratios show that the model is capable of producing term structures of probabilities of default that are consistent with some empirical findings. This model could provide new insight for future research on corporate bond analysis and credit risk measurement.