5In this paper we give a method for computing the fair insurance fee associated with the 6 guaranteed minimum death benefit (GMDB) clause included in many variable annuity contracts.
7We allow for partial withdrawals, a common feature in most GMDB contracts, and determine 8 how this affects the GMDB fair insurance charge. Our method models the GMDB pricing procedure is included. We show that the discrete equations are stable, monotone and consistent
13and hence obtain convergence to the unique, continuous viscosity solution, assuming this exists.14 Our results show that the addition of the partial withdrawal feature significantly increases the 15 fair insurance charge for GMDB contracts.
Infinite reload options allow the user to exercise his reload right as often as he chooses during the lifetime of the contract. Each time a reload occurs, the owner receives new options where the strike price is set to the current stock price. We consider a modified version of the infinite reload option contract where the strike price of the new options received by the owner is increased by a certain percentage; we refer to this new contract as an increased reload option. The pricing problem for this modified contract is characterized as an impulse control problem resulting in a Hamilton-Jacobi-Bellman equation. We use fully implicit timestepping and prove that the discretized equations are monotone, stable and consistent, implying convergence to the viscosity solution. We also derive a globally convergent iterative method for solving the non-linear discrete equations. Numerical examples show that both the exercise policy and the option value are very sensitive to the percentage increase in the reload strike.
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