Pricing Longevity Bonds using Implied Survival Probabilities

For annuity providers, longevity risk, i.e. the risk that future mortality trends differ from those anticipated, constitutes an important risk factor. In order to manage this risk, new financial products will be needed. One of the basic building blocks for such mortality backed securities is the so-called survivor or longevity bond, the future payments of which depend on the survival rates of a certain population. We propose a methodology for the modeling and pricing of longevity bonds. We generalize the ideas of Lin and Cox (2005) and show how to derive implied survival probabilities from annuity market quotes. Taking those implied survival probabilities as a starting point, we derive the price and the dynamics of longevity bonds by applying the Heath-Jarrow-Morton framework for mortality modeling building on an idea proposed by Miltersen and Persson (2005). We show how the models within our framework can be calibrated and applied for pricing mortality derivatives.