Peter Hieber

Abstract: Randomization is a technique in Finance to replace known quantities (like the time to maturity) by random variables. This sometimes gives moments or quantiles of the payoff in closed-form, avoiding any kind of integration, Fourier inversion or simulation algorithm. We apply this idea to insurance and Guaranteed Minimum Death Benefits (GMDB) where payoff dates are per se random. The remaining lifetime is expanded in terms of a Laguerre series while the financial market follows a regime switching model with two-sided phase-type jumps. For European-type GMDBs, we obtain the density of the payoff in closed form as a Laurent series. Payoff distributions of contracts with path-dependent guarantee features can be expressed in terms of solutions of Sylvester equations (=matrix equations of the form AX + XB =C).

This is joint work with Griselda Deelstra (Université Libre de Bruxelles).

A paper version is available here: Deelstra, Griselda and Hieber, Peter, Randomization and the Valuation of Guaranteed Minimum Death Benefits, https://ssrn.com/abstract=4115505.