On the Risk of Insurance Liabilities: Debunking Some Common Pitfalls

Abstract

The objective of this paper is to contribute to a better understanding of the driving forces of a life insurance company. More specifically, the issues of the duration and convexity of insurance liabilities and equity are addressed. These issues deserve a careful rethinking given the recent trends that have affected the insurance landscape. A correct assessment of these risk measures is critical as they constitute the primary ingredients of any sound asset-liability management approach. In addition, the effort toward a more detailed and more accurate risk picture of life insurance operations enables one to debunk some pitfalls that are commonly encountered in the insurance industry.

Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment

“…In this section, as in Bauer et al (2006), we let the guaranteed interest rate g = 3.5%, the minimum participation rate δ = 90%, the minimum portion of market value earnings that has to be displayed as book value earnings in the balance sheet y = 50%, the target rate z = 5%, the reserve corridor [a, b] = [5%, 30%], the portion of earnings that is provided to equity holders α = 5%, and the volatility of the asset portfolio σ A = 7.5%. Furthermore, we set the volatility of the Ornstein-Uhlenbeck process σ r = 1% as in Briys and de Varenne (1997) and the correlation ρ = 0.05, which corresponds to a proportion of about 10% − 15% of stock in the asset portfolio. 6 In order to obtain comparable results for the Vasicek (1977) and the Cox et al (1985) model, we equate the variances of the corresponding processes under r 0 , which leads to a volatility parameterσ r = σ 2 r ξ for the square root process within the Cox et al (1985) model.…”

“…In contrast, other publications allow for a stochastic evolution of interest rates. However, these articles consider point-to-point guarantees rather than cliquet style guarantees (see Barbarin and Devolder (2005), Bernard et al (2005), or Briys and de Varenne (1997)), or do not allow for the consideration of typical distribution schemes or option features embedded in many life insurance contracts (see, e.g., Miltersen and Persson (1999)). …”

A general asset–liability management model for the efficient simulation of portfolios of life insurance policies

“…The same two-factor model is used in [11]. In [8,20], the Vasicek model is employed instead of the CIR model. In [22] stocks and bonds are modelled via a coupled system of two geometric Brownian motions with different drift and volatility parameters.…”

“…For p = r 0 this measure of sensitivities is also called effective duration or interest-rate elasticity. For a discussion and further collection of useful risk measures we refer, e.g., to [8,11,19].…”

“…This task can be achieved by performing stochastic simulations of ALM models in a risk-neutral environment. Much effort has been spent on the development of such models in the last years, see, e.g., [1,2,8,11,14,15,16,22,24,27] and the references therein. Thereby, most authors focus on the fair valuation and contract design of unit-linked and participating life insurance policies.…”