Improved Precision in Calibrating CreditRisk $${^+}$$ + Model for Credit Insurance Applications

Credit insurance is a type of non-life insurance which protects the insured against insolvency events that may arise from all their buyers during the contract period. Dependency amongst claims generated by the underlying buyers is a critical issue in credit insurance modeling, both for pricing and risk management purposes. Given the similarity between a basket of exposures arising from invoices issued to risky buyers and a financial risky obligations portfolio, CreditRisk $$^+$$ + model has been applied to credit insurance multiple times in literature, although having been originally developed for the banking sector. In CreditRisk $$^+$$ + framework, claims are represented by a doubly stochastic process, where the dependency amongst expected default frequencies is described by a multivariate Clayton copula. However, calibration of this dependence structure in credit insurance requires to extract the information embedded in the historical database of an insurance company, given the lack of financial markets data which are available to banks about their debtors. We investigate how to estimate the copula parameters by historical claims time series and how the estimation precision scales with sampling frequency of the time series used in the calibration.