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The modelling of defaults in the finance industry: A succinct overview of types of default models commonly used in the finance industry and the links between them

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This book focuses on the estimation and modelling of defaults, both for firms and for specific types of loans and debt instruments. It provides a comprehensive overview of the default models most widely used in finance and risk management in a self-contained way, with consistent notations across the various models, revealing the links between models as well as each model's use, limitations and extensions. The book also presents two new and less well-known promising types of models for estimating and predicting defaults. The two models are tested in this book using data on the performance of Spanish small and medium sized (SME) loans in Asset Backed Securities (ABS), in particular loan-level data stored in the European Data Warehouse. The first type of innovative model borrows techniques from the speech recognition literature to estimate the credit cycle of a particular sector of the economy based on a time series of realised defaults. Our results confirm that most sectors go through "credit cycles", which can be distinct from business cycles and estimated independently from traditional macro-economic variables if long-enough time series of realised defaults are available. Within each phase of the cycle (low default risk / high default risk), the model is able to efficiently estimate different probability of defaults for loans belonging to that sector, using data from Bloomberg. The required efficient algorithms are provided in an annex and are crucial to the implementation of the model, as direct computation is not achievable. The second type of innovative model borrows techniques from survival analysis literature to allow for more granular default probability estimations, using loan-level data from Spanish SME ABS transactions. Our model uses rigorous statistical methods traditionally used in medicine, but largely unknown in finance, to produce loan-specific relative risk assessments, leveraging the very large data set to achieve granular estimations. We estimated risk scores that quantify each characteristic of an individual loan in terms of how much it increases the probability of default, holding all other characteristics, as well as some selected macro-economic variables, constant. Of all the loan characteristics that were tested, we find that the loan purpose is the most relevant for the risk of default, with "debt-consolidation" increasing twofold the rate of default compared to loans whose purpose was for investment, i.e. "purchase of equipment". The legal form, the borrower's Basel 3 segment, the type of collateral used, as well as the initial interest spread charged to the borrower at origination of the loan, are also crucial explanatory variables in Spanish SME loan riskiness, with the impact on the default rate being of a similar magnitude than a 1% variation of the Gross-Domestic Product (GDP).

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