On Surrender and Default Risks

Abstract

This article examines certain types of saving institutions or insurance companies that are subject to surrender and default risks, in a stochastic interest rate context. In the setting under study, investors are endowed with an option to surrender. The goal of the article is to study how this option impacts the default risk of the issuing company and the value of the contracts it issues. Surrender risk has been extensively studied in arbitrated markets, using trees or least-squares Monte-Carlo methods for valuations, although practitioners often rely on econometric methods. We deal with surrender risk in a third way, assuming policyholders have sets of information and preferences that differ from those of financial market agents, but without relying on econometric methods. In particular, policyholders are supposed to be only partially rational (at least in the financial sense). This is done by modeling surrender risk through a Cox process correlated to the assets and interest rate dynamics. The article provides formulas for the dynamics of the assets of the issuing firm (these dynamics drive the default time of the company), and for the valuation of liabilities and equity. A numerical illustration is provided.

Keywords: Surrender risk, default risk, interest rate risk, Cox process, participating policies