On the pricing of the GLWB option in a Variable Annuity contract

Abstract

This paper proposes a valuation model for the GLWB option using tractable financial and stochastic mortality processes in a continuous time framework. The policy has been analyzed assuming a static approach, in which policy holders withdraw each year just the guaranteed amount. Specifically we have considered as basic model the one proposed by Fungetal. (2014) and then we have generalized it introducing more realistic assumptions. In particular, we have taken into account a CIR stochastic process for the term structure of interest rates and a Heston model for the volatility of the underlying account, analyzing their effect on the fair price of the contract. We have addressed these two hypotheses separately at first, and jointly afterwards. As part of our analysis, we have implemented the theoretical model using a Monte Carlo approach. To this end, we have created ad hoc codes based on the programming language MATLAB, exploiting its fast matrix-computation facilities", DEAMS Research Paper Series 2014, N° 1, Trieste, EUT Edizioni Università di Trieste, 2015, pp.29