Multi-period Factor Model of a Loan Portfolio

0480803 - ÚTIA 2018 CZ eng V - Výzkumná zpráva
Šmíd, Martin - Dufek, J.
Multi-period Factor Model of a Loan Portfolio.
Praha: ÚTIA AV ČR v.v.i, 2017. 45 s. Research Report, 2363.
Klíčová slova: Credit Risk * Structural Factor Models * Loan Portfolio Management
http://library.utia.cas.cz/separaty/2017/E/smid-0480803.pdf

We construct a general dynamic model of losses of a large loan portfolio, secured by collaterals. In the model, the wealth of a debtor and the price of the corresponding collateral depend each on two factors: a common one, having a general distribution, and an individual one, following an AR(1) process. The default of a loan happens if the wealth stops to be su cient for repaying the loan. We show that the mapping transforming the common factors into the probability of default (PD) and the loss given default (LGD) is one-to-one twice continuously differentiable. As the transformation is not analytically tractable, we propose a numerical technique for its computation and demonstrate its accuracy by a numerical study.
We show that the results given by our multi-period model may differ signi cantly from
those resulting from single-period models, and demonstrate that our model naturally replicates
the empirically observed decrease of PDs within a portfolio in time. In addition, we give a formula for the overall loss of the portfolio and, as an example of its application, we formulate a simple optimal scoring decision problem and discuss its solution.
Trvalý link: http://hdl.handle.net/11104/0276487