Minisymposium: Jeunes chercheurs en mathématiques financières
State-Dependent Fees and the Surrender Option in Variable Annuities
MacKay, Anne, Carole Bernard and Mary Hardy
University of Waterloo

Guaranteed minimum maturity benefits (GMMB) are similar to financial options on the fund value of a variable annuity. They are usually financed through a fee set as a fixed percentage of the fund, which is paid continuously throughout the term of the contract. From the policyholder's point of view, when the option is deep out-of-the-money, this fixed fee represents an important incentive to lapse. We first present an integral form for the value of a contract with a surrender option, and we analyse the optimal surrender region. We discuss the link between the continuous fee and the value of the surrender option, and present ideas for more advanced fee structures that aim to decrease the value of the surrender option, thus reducing the incentive to lapse. In particular, we introduce a new type of fee structure for variable annuities, where the fee rate depends on the moneyness of the guarantee. We present some numerical examples and sensitivity analysis.

Lundi, 17 juin, 15h30
Salle Du Jardin