A novel approach to rating transition modelling via Machine Learning and SDEs on Lie groups
This work addresses rating transition modeling for finance and risk management, presenting a novel geometric approach that is incremental in combining existing methods like SDEs and deep learning.
The paper tackles the problem of modeling rating transitions by introducing a stochastic process on matrix Lie groups to ensure valid rating matrices, and calibrates it using a TimeGAN deep neural network to fit historical data, achieving a good fit as demonstrated by satisfying key properties of rating matrix time series.
In this paper, we introduce a novel methodology to model rating transitions with a stochastic process. To introduce stochastic processes, whose values are valid rating matrices, we noticed the geometric properties of stochastic matrices and its link to matrix Lie groups. We give a gentle introduction to this topic and demonstrate how Itô-SDEs in R will generate the desired model for rating transitions. To calibrate the rating model to historical data, we use a Deep-Neural-Network (DNN) called TimeGAN to learn the features of a time series of historical rating matrices. Then, we use this DNN to generate synthetic rating transition matrices. Afterwards, we fit the moments of the generated rating matrices and the rating process at specific time points, which results in a good fit. After calibration, we discuss the quality of the calibrated rating transition process by examining some properties that a time series of rating matrices should satisfy, and we will see that this geometric approach works very well.