Time-consistent evaluation of credit risk with contagion
(2022) Journal of Computational and Applied Mathematics — Vol. 403, p. 113848 (2022)
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- Abstract
- A time-consistent evaluation is a dynamic pricing method according to which a risk that will be almost surely cheaper than another one at a future date should already be cheaper today. Common actuarial pricing approaches are usually not time-consistent. Pelsser and Ghalehjooghi (2016) derived time-consistent valuation principles from time-inconsistent ones. The aim of this paper is twofold. Firstly, we propose a model for credit insurance portfolios taking into account the contagion risk via self-exciting jump processes. Secondly, we extend the approach of Pelsser and Ghalehjooghi to credit insurance in this framework. Starting from classical time-inconsistent actuarial pricing methods, we derive partial integro-differential equations (PIDE) for their time-consistent counterparts. We discuss numerical methods for solving these PIDEs and their results. We draw two conclusions from these results. On the one hand, we show that time-consistent evaluations tend to give higher prices, compared to time-inconsistent evaluations. On the other hand, our results show that the time-consistency of evaluations allows to better take into account the risk of contagion in credit insurance, if such a risk exists. Finally, we propose a method to calibrate our model and use it in practice.
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Ketelbuters, J. J., & Hainaut, D. (2022). Time-consistent evaluation of credit risk with contagion. Journal of Computational and Applied Mathematics, 403, 113848. https://doi.org/10.1016/j.cam.2021.113848 (Original work published 2022)