Capital forbearance and premiums for insurance guaranty funds

Abstract

A multiperiod model is developed to measure the cost of guaranty funds for insurers by incorporating interest rate risk, catastrophe risk, timing of liquidation and moral hazard. Since not all inadequately capitalized insurers are resolved immediately, the unresolved failing insurers can continue to operate under the coverage of the guaranty funds and hence increase insurance costs of the industry The guaranty contract can be viewed as a put option with stochastic strike price and maturity, and can induce moral hazard behavior. Although there exists no closed-form formula for our model, Monte Carlo simulations can be used to compute the guaranty value. Our numerical method is novel in the sense that we simplify the higher-dimensional simulation problem via first partially solving two stochastic differential equations. Our results show how the fair premium rate can be affected by the length of the intended coverage horizon, regulatory capital forbearance, moral hazard, interest rate uncertainty, and credit and catastrophe risks.