Indifference pricing of insurance-linked securities in a multi-period model

Abstract

Insurance-linked securities (ILS) have recently become an important risk transfer mechanism to help insurers and reinsurers transfer catastrophe risks to the capital market. We employ the utility indifference approach to establish a pricing framework for a representative agent who trades an ILS with payoff linked to an insurance risk process and a reference rate process. The agent, while investing in a financial market composed of traditional financial instruments, discovers her indifference prices of the ILS by weighing the ILS trade on her exponential utility. The problem has been studied extensively, but mainly in one-period models that are best suited for zero-coupon instruments. In view of the prevalence of ILS with interim payments, we extend the study to a multi-period model by working with time 0 equivalent values and solving a multi-period optimization problem. We offer insights into issues such as coherence and time consistency of the ask and bid indifference prices obtained. Finally, we conduct a sensitivity analysis of the prices against certain risk parameters.