A new methodology to avoid high variation in reserves for insurers and reinsurers

A short note:

Forecasting NATCAT reserves using the CIR2 model

By Giuseppe Orlando and Michele Bufalo

MICHELE BUFALO works in the Department of Methods and Models for Economics, Territory and Finance at Sapienza Università di Roma.
GIUSEPPE ORLANDO works in the Department of Economics and Finance at Università degli Studi di Bari Aldo Moro.


In this note we highlight some features of the CIR2 model we have developed, which is a generalised two-factor square root model (i.e. a model where, under certain conditions, both losses and volatility are positive and where volatility increases with the level of loss). In the framework we present, calculation of the mean and variance of loss are correlated processes; this is a new theoretical approach, and difficult to implement insofar as there are no closed-form solutions. This methodology is designed primarily for use by insurers and reinsurers that need to avoid high variation in their reserves; however, it could be extended to apply to any business that is exposed to extreme events and aims to preserve a stable cash flow to shareholders. In fact, though generalised linear models are common instruments in the pricing of nonlife insurance contracts, they are inadequate for extreme claims. As such, the suggested model could be helpful for pricing in this instance.


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This article represents the opinion of the authors, and not necessarily the opinion of the AAE.

This article was published in The European Actuary No. 29 – March 2021