Non-linearity and the distribution of market-based loss rates

Abstract We synthesize the extended linear beta regression with a neural network structure to model and predict the mean and precision of market-based loss rates. We can incorporate non-linearity in mean and precision in a flexible way and resolve the problem of specifying the underlying form in advance. As a novelty, we can show that the proportion of non-linearity for the mean estimates is $$14.10\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>14.10</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> and $$80.37\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>80.37</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> for the precision estimates. This implies that especially the shape of the loss rate distribution entails a large amount of non-linearity and, thus, our approach consistently outperforms its linear counterpart. Furthermore, we derive trainable activation functions to allow a data-driven estimation of their shape. This is important if predictions have to be in a certain interval, e.g., (0, 1) or $$(0,\infty )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . Conducting a scenario analysis, we observe that our estimated distributions are more refined compared to traditional models, thereby demonstrating their suitability for risk management purposes. These estimated distributions can assist financial institutions in better identifying diverse risk profiles among their creditors and across various macroeconomic states.