Modelling default risk through macroeconomic factor evolution
Problem raised by Management Solutions
Coordinators:
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 multiperiod 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.