Economic Pricing of Mortality-Linked Securities
In previous research on pricing mortality-linked securities, the no-arbitrage approach is often used. However, this method, which takes market prices as given, is difficult to implement in today's embryonic market where there are few traded securities. In particular, with limited market price data, identifying a risk neutral measure requires strong assumptions. In this thesis, we approach the pricing problem from a different angle by considering economic methods. We propose pricing approaches in both competitive market and non-competitive market. In the competitive market, we treat the pricing work as a Walrasian tâtonnement process, in which prices are determined through a gradual calibration of supply and demand. Such a pricing framework provides with us a pair of supply and demand curves. From these curves we can tell if there will be any trade between the counterparties, and if there will, at what price the mortality-linked security will be traded. This method does not require the market prices of other mortality-linked securities as input. This can spare us from the problems associated with the lack of market price data. We extend the pricing framework to incorporate population basis risk, which arises when a pension plan relies on standardized instruments to hedge its longevity risk exposure. This extension allows us to obtain the price and trading quantity of mortality-linked securities in the presence of population basis risk. The resulting supply and demand curves help us understand how population basis risk would affect the behaviors of agents. We apply the method to a hypothetical longevity bond, using real mortality data from different populations. Our illustrations show that, interestingly, population basis risk can affect the price of a mortality-linked security in different directions, depending on the properties of the populations involved. We have also examined the impact of transitory mortality jumps on trading in a competitive market. Mortality dynamics are subject to jumps, which are due to events such as the Spanish flu in 1918. Such jumps can have a significant impact on prices of mortality-linked securities, and therefore should be taken into account in modeling. Although several single-population mortality models with jump effects have been developed, they are not adequate for trades in which population basis risk exists. We first develop a two-population mortality model with transitory jump effects, and then we use the proposed mortality model to examine how mortality jumps may affect the supply and demand of mortality-linked securities. Finally, we model the pricing process in a non-competitive market as a bargaining game. Nash's bargaining solution is applied to obtain a unique trading contract. With no requirement of a competitive market, this approach is more appropriate for the current mortality-linked security market. We compare this approach with the other proposed pricing method. It is found that both pricing methods lead to Pareto optimal outcomes.