Valuation Of Life Insurance Contracts Research Articles

Aggregate lapsation risk

We study aggregate lapsation risk in the life insurance sector. We construct two lapsation risk factors that explain a large fraction of the common variation in lapse rates of the 30 largest life insurance companies. The first is a cyclical factor that is positively correlated with credit spreads and unemployment, while the second factor is a trend factor that correlates with the level of interest rates. Using a novel policy-level database from a large life insurer, we examine the heterogeneity in risk factor exposures based on policy and policyholder characteristics. Young policyholders with higher health risk in low-income areas are more likely to lapse their policies during economic downturns. We explore the implications for hedging and valuation of life insurance contracts. Ignoring aggregate lapsation risk results in mispricing of life insurance policies. The calibrated model points to overpricing on average. In the cross-section, young, low-income, and high-health risk households face higher effective mark-ups than the old, high-income, and healthy.

Valuation of contingent claims with stochastic interest rate and mortality driven by Lévy processes

In this paper, we consider a model with stochastic interest rate and stochastic mortality, which is driven by a Lévy process. Under the assumption that the stochastic mortality and interest rate are dependent, we discuss the valuation of life insurance contracts. Employing the method of change of measure together with the Bayes’ rule, we present the pricing formulas in closed form for the survival and death benefit models. Finally, numerical experiments illustrate the effects of some parameters.

Fair Valuation of Life Insurance Contracts Under a Two-Sided Jump Diffusion Model

In this article, we study the fair valuation of participating life insurance contract, which is one of the most common life insurance products, under the two-sided jump diffusion model with the consideration of default risk. The participating life insurance contracts considered here can be expressed as portfolios of options as shown by Grosen and Jøgrgensen (1997). We can give the Laplace transforms for these options under the two-sided jump diffusion model, and then price these options by inverting Laplace transforms.

On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View

AbstractIn recent years, market-consistent valuation approaches have gained an increasing importance for insurance companies. This has triggered an increasing interest among practitioners and academics, and a number of specific studies on such valuation approaches have been published.In this paper, we present a generic model for the valuation of life insurance contracts and embedded options. Furthermore, we describe various numerical valuation approaches within our generic setup. We particularly focus on contracts containing early exercise features since these present (numerically) challenging valuation problems.Based on an example of participating life insurance contracts, we illustrate the different approaches and compare their efficiency in a simple and a generalized Black-Scholes setup, respectively. Moreover, we study the impact of the considered early exercise feature on our example contract and analyze the influence of model risk by additionally introducing an exponential Lévy model.

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

Over the last years, the valuation of life insurance contracts using concepts from financial mathematics has become a popular research area for actuaries as well as financial economists. In particular, several methods have been proposed of how to model and price participating policies, which are characterized by an annual interest rate guarantee and some bonus distribution rules. However, despite the long terms of life insurance products, most valuation models allowing for sophisticated bonus distribution rules and the inclusion of frequently offered options assume a simple Black–Scholes setup and, more specifically, deterministic or even constant interest rates. We present a framework in which participating life insurance contracts including predominant kinds of guarantees and options can be valuated and analyzed in a stochastic interest rate environment. In particular, the different option elements can be priced and analyzed separately. We use Monte Carlo and discretization methods to derive the respective values. The sensitivity of the contract and guarantee values with respect to multiple parameters is studied using the bonus distribution schemes as introduced in [Bauer, D., Kiesel, R., Kling, A., Ruß, J., 2006. Risk-neutral valuation of participating life insurance contracts. Insurance: Math. Econom. 39, 171–183]. Surprisingly, even though the value of the contract as a whole is only moderately affected by the stochasticity of the short rate of interest, the value of the different embedded options is altered considerably in comparison to the value under constant interest rates. Furthermore, using a simplified asset portfolio and empirical parameter estimations, we show that the proportion of stock within the insurer’s asset portfolio substantially affects the value of the contract.

Risk-neutral valuation of participating life insurance contracts

The valuation of life insurance contracts using concepts from financial mathematics has recently attracted considerable interest in academia as well as among practitioners. In this paper, we will investigate the valuation of participating contracts, which are characterized by embedded interest rate guarantees and some bonus distribution rules. We will model these under the specific regulatory framework in Germany; however, our analysis can be applied to any insurance market with cliquet-style guarantees. We will present a framework, in which different kinds of guarantees or options can be analyzed separately. Also, the practical implementation of such models is discussed. We use two different numerical approaches to derive fair parameter settings of such contracts and price the embedded options. The sensitivity of the contract value with respect to multiple parameters is studied. In particular, we find that life insurers offer interest rate guarantees below their risk-neutral value. Furthermore, the financial strength of an insurance company considerably affects the value of a contract.

Affine processes for dynamic mortality and actuarial valuations

We address the risk analysis and market valuation of life insurance contracts in a jump-diffusion setup. We exploit the analytical tractability of affine processes to deal simultaneously with financial and demographic risks affecting a wide range of insurance covers. We then focus on mortality at pensionable ages and show how the risk of longevity can be taken into account. A parallel with the pricing of certain credit risky securities is drawn, in order to employ important results derived in that field.

Affine Processes for Dynamic Mortality and Actuarial Valuations

We address the risk analysis and market valuation of life insurance contracts in a jump-diffusion setup. We exploit the analytical tractability of affine processes to deal simultaneously with financial and demographic risks affecting a wide range of insurance covers. We then focus on mortality at pensionable ages and show how the risk of longevity can be taken into account. A parallel with the pricing of certain credit risky securities is drawn, in order to employ important results derived in that field.

Valuation of Life Insurance Contracts with Surrender Options

The paper derives a recursive algorithm for pricing life insurance policies in the case where interest rates are stochastic and the insured can surrender his policy for cash at any time at a pre-specified surrender value. This is done under the assumption that the insured is rational, and alternatively, under the assumption that the surrender rate is an exogenously specified function of the loss from a non-optimal surrender. The pricing methodology is adapted from the literature on valuation of defaultable securities, where default is analogous to the death of the insured.