Provisioning against borrowers default risk

Geoffrey Nichil (1) , Pierre Vallois (2, 1)

1 IECL - Institut Élie Cartan de Lorraine
2 BIGS - Biology, genetics and statistics

This paper focuses on the risk of loan default from the point of view of an insurer required to indemnify a bank for losses resulting from a borrower defaulting. The main objective of this paper is to model the provision (or claim reserve) against the risk of borrowers defaulting. Unlike traditionally used models, our model depends on specific information concerning the borrowers (amount borrowed and term of loan). Our approach will also take into account three kinds of dependence: the dependence between each claim amount (by taking into account the real estate price), the dependence between the date of default and the claim amount, and the dependence between the number of defaults and the claim amount. Both theoretical and applied, our model allows the calculation of the mean, the variance, and the law of the provision. The amount of data available allows us to estimate all the parameters and to calculate the mean and the variance plus the quantiles of the provision.

Mots clés: Borrower default risk; Time of default; Individual stochastic provisioning; Geometric Brownian motion; Poisson point process; Quantile

Domaines: Probabilités [math.PR]

Geoffrey Nichil, Pierre Vallois. Provisioning against borrowers default risk. Insurance: Mathematics and Economics, 2016, 66, pp.29-43. ⟨10.1016/j.insmatheco.2015.10.004⟩. ⟨hal-01224520⟩