TITLE:
Further Results about Calibration of Longevity Risk for the Insurance Business
AUTHORS:
Mariarosaria Coppola, Valeria D’Amato
KEYWORDS:
Solvency II; Solvency Capital Requirement; Longevity Risk; Longevity Shocks; Expected Shortfall
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.4,
March
10,
2014
ABSTRACT:
In life insurance business, longevity risk, i.e. the risk that the insured population lives longer than the
expected, represents the heart of the risk assessment, having significant
impact in terms of solvency capital requirements (SCRs) needed to front the
firm obligations. The credit crisis has shown that systemic risk as longevity
risk is relevant and that for many insurers it is actually the dominant risk.
With the adoption of the Solvency II directive, a new area for insurance in
terms of solvency regulation has been opened up. The international guidelines
prescribe a market consistent valuation of balance sheets, where the solvency
capital requirements to be set aside are calculated according to a modular
structure. By mapping the main risk affecting the insurance portfolio, the
capital amount able to cover the liabilities corresponds to each measured risk.
In Solvency II, the longevity risk is included into underwriting risk
module. In particular, the rules propose that companies use a standard model
for measuring the SCRs. Nevertheless, the legislation under consideration
allows designing tailor-made internal models. As regards the longevity risk
assessment, the regulatory standard model leads to noteworthy inconsistencies.
In this paper, we propose a stochastic volatility model combined
with a so-called coherent risk measure as the expected shortfall for measuring
the SCRs according to more realistic assumptions on future evolution of
longevity trend. Finally empirical evidence is provided.