A two-decrement model for the valuation and risk measurement of a guaranteed annuity option

Abstract

The lapse risk arising from the termination of policies, due to a variety of causes, has significant influence on the prices of contracts, liquidity of an insurer, and the reserves necessary to meet regulatory capital. The aim is to address in an integrated manner the problem of pricing and determining the capital requirements for a guaranteed annuity option when lapse risk is embedded in the modelling framework. In particular, two decrements are considered in which death and policy lapse occurrences with their correlations to the financial risk are explicitly modelled. A series of probability measure changes is employed and the corresponding forward, survival, and risk-endowment measures are constructed. This approach superbly circumvents the rather slow “simulation-within-simulation” pricing procedure under a stochastic setting. Implementation results illustrate that the proposed approach cuts down the Monte-Carlo simulation technique’s average computing time by 99%. Risk measures are computed using the moment-based density method and benchmarked against the Monte-Carlo-based numerical findings. Depending on the risk metric used (e.g., VaR, CVaR, various forms of distortion risk measures) and the correlation between the interest and lapse rates, the capital requirement may substantially change, which could be either an increase or decrease of up to 50%.