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 2021004, LIDAM Discussion Papers 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 PIDE and their results. We draw two conclusions from these results. On the one hand, we show that working with time-consistent evaluations in the absence of a risk of contagion does not make a significant difference compared to time-inconsisent evaluations. On the other hand, our results show that the time-consistency of evaluations allows to better take into acount the risk of contagion in credit insurance, if such a risk exists.

Keywords: Credit risk; Self-exciting processes; Time-consistency (search for similar items in EconPapers)
Pages: 22
Date: 2021-01-01
New Economics Papers: this item is included in nep-ias and nep-rmg
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