We consider discrete default intensity based and logit type reduced form models for conditional default probabilities for corporate loans where we develop simple closed form approximations to the maximum likelihood estimator (MLE) when the underlying covariates follow a stationary Gaussian process. In a practically reasonable asymptotic regime where the default probabilities are small, say 1% annually, the number of firms and the time period of data available is reasonably large, we rigorously show that the proposed estimator behaves similarly or slightly worse than the MLE when the underlying model is correctly specified. For more realistic case of model misspecification, both estimators are seen to be equally good, or equally bad. Further, beyond a point, both are more-or-less insensitive to increase in data. These conclusions are validated on empirical and simulated data. The proposed approximations should also have applications outside finance, where logit-type models are used and probabilities of interest are small.
Anand Deo is a PhD candidate in the School of Technology and Computer Science at the Tata Institute of Fundamental Research, Mumbai, India. He received a Bachelor’s degree in Electronics Engineering from Mumbai University. His research interests are broadly in applied probability, and specifically in finance and Operations Research. His past work develops efficient parameter estimation techniques in the rare event setting, and he is currently working on understanding the behaviour of large, inter-connected banking networks.
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