Signs of dependence and heavy tails in non-life insurance data

TL;DR

This study analyzes Swedish non-life insurance data to understand loss distributions and dependencies, revealing weaker inter-line dependence than standard models assume and highlighting implications for internal versus standard SCR calculation methods.

Contribution

The paper provides new insights into loss dependence structures and their impact on SCR modeling, using pooled data and actuarial loss definitions for improved accuracy.

Findings

Dependence between lines of business is weaker than in Solvency II assumptions.

Dependence between companies may influence financial stability assessments.

Internal models may outperform standard formulas under certain conditions.

Abstract

In this paper we study data from the yearly reports the four major Swedish non-life insurers have sent to the Swedish Financial Supervisory Authority (FSA). We aim at finding marginal distributions of, and dependence between, losses on the five largest lines of business (LoBs) in order to create models for Solvency Capital Requirement (SCR) calculation. We try to use data in an optimal way by sensibly defining an accounting year loss in terms of actuarial liability predictions, and by pooling observations from several companies when possible to decrease the uncertainty about the underlying distributions and their parameters. We find that dependence between LoBs is weaker in our data than what is assumed in the Solvency II standard formula. We also find dependence between companies that may affect financial stability, and must be taken into account when estimating loss distribution parameters. Moreover, we discuss under what circumstances an insurer is better (or worse) off using an internal model for SCR calculation instead of the standard formula.