The Rating Scale Paradox: An Application to the Solvency 2 Framework
Abstract
:1. Introduction
2. A Rating System with Hybrid Rating Scale
2.1. A Typical Rating System
2.2. A Hybrid Partition Criterion
3. A Credit Insurance Company under the Solvency 2 Regulatory Framework
3.1. Elements of Credit Insurance
3.2. A Credit Insurance RAF in the Solvency 2 Framework
- i.
- The Premium Risk, whose SCR is measured as
- ii.
- The Catastrophe Recession Risk, whose SCR is measured as
- iii.
- The Catastrophe Default Risk, whose SCR is measured as
4. Benefits of the Hybrid Rating Scale to a Solvency 2 Based RAF
4.1. as the Solution of an Optimization Problem
4.2. A Full Working Example
4.3. Sensitivity Analysis
5. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
References
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Variable | Description | Value |
---|---|---|
P | Premiums to be earned during the next 12 months (arbitrary units) | |
D | SCR associated to Catastrophe Default risk in Solvency 2 Standard Formula framework (arbitrary units) | |
Risk appetite per risk expressed as the maximum acceptable contribution to the ( units) | 5 | |
k | Average effect of contractual clauses and conditions | |
ℓ | Average exposure at default ratio | |
c | Insurer’s cost ratio | |
Target return required by the insurer’s stakeholders | ||
Risk free return | ||
R | Number of notches belonging to the considered master scale | 10 |
Notch associated with the minimum acceptable creditworthiness per buyer | 7 | |
N | Number of risky buyers against whom the insured sellers ask for protection | |
Expected value of the buyers’ PD distribution | ||
Standard deviation of the buyers’ PD distribution |
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Giacomelli, J. The Rating Scale Paradox: An Application to the Solvency 2 Framework. Standards 2023, 3, 356-372. https://doi.org/10.3390/standards3040025
Giacomelli J. The Rating Scale Paradox: An Application to the Solvency 2 Framework. Standards. 2023; 3(4):356-372. https://doi.org/10.3390/standards3040025
Chicago/Turabian StyleGiacomelli, Jacopo. 2023. "The Rating Scale Paradox: An Application to the Solvency 2 Framework" Standards 3, no. 4: 356-372. https://doi.org/10.3390/standards3040025