Fig 4.4 - four models

With this exercise the fair fee for VAs with GMAB and GMDB riders will be found by means of the static approach. The caracteristics of the contracts are the following:

• Contract expires at T = 15 years
• Age of the policyholder at contract inception in 50
• Both GMAB and GMDB pay the minimum amount as the roll-up of premium.
• The roll-up rate is 1%
• The fee is state-dependent
• The initial state-dependent barrier is the GMAB minimum amount at T = 15 indicated with G

We are going to progressively increase the barrier with the formula (1 + k) * G where k varies from 0 to 1 with step 0.1

With regards to the simulation:

• The number of Monte Carlo simulations will be 20000.
• Financial processes and intensity of mortality follow the SDEs in BMOP2011. This is model 4

##  [1] 0.04234375 0.03250000 0.02687500 0.02406250 0.02195313 0.01984375
##  [7] 0.01843750 0.01843750 0.01703125 0.01703125 0.01632812 0.01421875

In the graph the dashed line corresponds to the constant fee case whose value is

## [1] 0.01421875

The following graph, model3 is assumed.

##  [1] 0.04375000 0.03250000 0.02687500 0.02406250 0.02125000 0.01984375
##  [7] 0.01843750 0.01843750 0.01703125 0.01703125 0.01632812 0.01421875

In the graph the dashed line corresponds to the constant fee case whose value is

## [1] 0.01421875

Graph for model 2

##  [1] 0.04937500 0.03812500 0.03250000 0.02968750 0.02687500 0.02406250
##  [7] 0.02265625 0.02125000 0.02125000 0.01984375 0.01984375 0.01562500

In the graph the dashed line corresponds to the constant fee case whose value is

## [1] 0.015625

Graph for model 1

##  [1] 0.04937500 0.04093750 0.03390625 0.02968750 0.02687500 0.02546875
##  [7] 0.02406250 0.02125000 0.02125000 0.02125000 0.01984375 0.01562500

In the graph the dashed line corresponds to the constant fee case whose value is

## [1] 0.015625