Reconceptualising the capital adequacy requirement of short-term insurance companies within the call option framework

Abstract

Conventional wisdom decrees that in order for insurers to provide cover, they require capital. One of the many methods of calculating capital requirements of short-term insurers is the insolvency put option framework. This technique was originally introduced by Merton (1977). The general argument is that bankruptcy occurs when shareholders exercise a valuable put option. Indeed, the corporation was introduced to protect shareholders from, mainly contractual, liabilities of persons who trade with the corporation. The corporation thus introduced the idea of limited liability of shareholders or as is often called the corporate veil. However, if a company defaults on its debt then equity holders have decided to allow an embedded call option to expire unexercised. As a result shareholders will behave as if they in fact hold a call option, which creates a different incentive than that suggested by the insolvency put idea. This study examines the role of capital and the influence of the insolvency put option within a short-term insurer. Specifically, it is argued that capital is not the cornerstone of a short-term insurer. Moreover, using Brownian motion and Itō calculus as well as continuous time financial models a more complete mathematical description of an insurance company is articulated by explicitly taking the embedded equity call option into account.