Modelling default risk through macroeconomic factor evolution
Problem raised by Management Solutions
Dr. Ignacio Villanueva (Facultad de Matemáticas, UCM)
Dr. Juan García Cascales (Management Solutions)
Fernando Prieto (Management Solutions)
Exposition of the problem:
In a highly changing macroeconomic environment, and quite particularly in times of severe financial distress like observed at the moment, it is essential for financial firms and investment banks to model the financial strength of their clients, in order to estimate the probability of recovering their investment.
One way of modelling the default probability of counterparties is by means of evolution index functions that describe dicotomic events in terms of systemic and idiosyncrasic variables. These functions may as well be decomposed as linear combinations of macroeconomics factors, leading to the default probability conditioned to a macroeconomic scenario.
Relating index function to macroeconomic factors has several open issues to be treated during the week, such as the modelling itself of macroeconomic factor evolution, alternatives to the conditioning function to take into account multi-period estimation or how to take into account credit quality migrations.
Scheme of the work to be done:
- Reading of basic papers to get familiar with the underlying default modelling and identifying fundamental macroeconomic factors.
- Modelling, by means of linear regression or similar structural equations, the relation of macroeconomic factors to the default probability. Analysis of macroeconomic time series.
- Adjustment of ARMA models to describe macroeconomic evolution, and implementation of a macroeconomic factor simulator, both conditioned to actual macroeconomic distress or using a random initial point.
- Implementation of the complete process: simulation of multiple macroeconomic scenarios and evaluation, on each, of transformation function to obtain a distribution of default probabilities.