Insurance guaranty premiums and exchange options

Abstract

Insurance guaranty schemes have been adopted to compensate policyholders for losses due to the insolvency of insurance companies. We derive explicit pricing formulas for risk-based premiums to focus on insurers' financial stability incorporating sudden changes of insurers' liabilities and asset-liability management (ALM) risk. The pricing formula of insurance guaranty fund is derived under regulatory forbearance. To deal with the insurance guaranty funds' payoff structure, this paper introduces new types of exchange options: early exchange options and barrier exchange options which allow multi-step boundaries. With these options, we can reflect jumps in value of underlying asset. Explicit pricing formulas are derived by using jump models with binomial approach. Also, we present sensitivity analysis on jump sizes, ALM risks and regulatory levels to provide guidance to financial authorities and insurers.