Time-consistent evaluation of credit risk with contagion

John-John Ketelbuters and Donatien Hainaut
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John-John Ketelbuters: Université catholique de Louvain, LIDAM/ISBA, Belgium
Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2021045, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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.

Keywords: Credit risk; Self-exciting processes; Time-consistency (search for similar items in EconPapers)
Pages: 17
Date: 2021-09-16
Note: In: Journal of Computational and Applied Mathematics, 2022, vol. 403, 113848
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2021045

DOI: 10.1016/j.cam.2021.113848

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