In a market where a stochastic interest rate component characterizes asset dynamics, we propose a flexible lattice framework to evaluate and manage options on equities paying discrete dividends and variable annuities presenting some provisions, like a guaranteed minimum withdrawal benefit. The framework is flexible in that it allows to combine financial and demographic risk, to embed in the contract early exercise features, and to choose the dynamics for interest rates and traded assets. A computational problem arises when each dividend (when valuing an option) or withdrawal (when valuing a variable annuity) is paid, because the lattice lacks its recombining structure. The proposed model overcomes this problem associating with each node of the lattice a set of representative values of the underlying asset (when valuing an option) or of the personal subaccount (when valuing a variable annuity) chosen among all the possible ones realized at that node. Extensive numerical experiments confirm the model accuracy and efficiency.

In the present work, we introduce a new numerical method based on a strong version of the mean-value theorem for integrals to solve quadratic Volterra integral equations and Fredholm integral equations of the second kind, for which there are theoretical monotonic non-negative solutions. By means of an equality theorem, the integral that appears in the aforementioned equations is transformed into one that enables a more accurate numerical solution with fewer calculations than other previously described methods. Convergence analysis is given.

This article proposes a bivariate lattice model for evaluating equity-linked policies embedding a surrender option when the underlying equity dynamics is described by a geometric Brownian motion with stochastic interest rate. The main advantage of the model stays in that the original processes for the reference fund and the interest rate are directly discretized by means of lattice approximations, without resorting to any additional transformation. Then, the arising lattices are combined in order to establish a bivariate tree where equity-linked policy premiums are computed by discounting the policy payoff over the lattice branches, and allowing early exercise at each premium payment date to model the surrender decision. © 2014 © 2014 Taylor & Francis

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