Securitization product valuations under multiple risk factors: the case of mortality bonds

We propose a flexible lattice model for pricing insurance contracts by considering both financial and actuarial risk factors. The simultaneous consideration of all such sources of risk is suggested by the fact that long-term policy benefits are influenced by the behaviour of all the variables involved in the product valuation. Consequently, the consideration of a stochastic process to model all the sources of risk is more appropriate for policy evaluations (see, for instance, Hilliard and Schwartz 1997 and Van-Haastrecht et al. 2009). Flexibility relies on the ability of the model to manage different specifications of the correlated processes governing interest rate and mortality in the analyzed case of mortality bonds. In this way, the insurer may make the most appropriate choices for the process dynamics. The model discretizes mortality and interest rate dynamics through two different binomial lattices and then combines them into a bivariate tree characterized by the presence of four branches for each node. The probability of each branch is defined to replicate the correlation affecting the two processes. Extensive numerical experiments assess the model accuracy by considering some stylized mortality bonds, but the model application is not limited to them being it able to manage different contract specifications.