Fig 4.4 - all 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 2%
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.

Model 1

##  [1] 0.06906250 0.05978125 0.05359375 0.04740625 0.04431250 0.04121875
##  [7] 0.03967188 0.03812500 0.03657813 0.03503125 0.03503125 0.02884375

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

## [1] 0.02884375

Model 2

##  [1] 0.06596875 0.05668750 0.05050000 0.04740625 0.04276563 0.04121875
##  [7] 0.03812500 0.03657813 0.03657813 0.03503125 0.03348438 0.02884375

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

## [1] 0.02884375

Model 3

##  [1] 0.05050000 0.04276563 0.03812500 0.03503125 0.03193750 0.03039063
##  [7] 0.02884375 0.02807031 0.02729688 0.02729688 0.02652344 0.02420313

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

## [1] 0.02420313

Model 4

##  [1] 0.05050000 0.04276563 0.03812500 0.03503125 0.03271094 0.03116406
##  [7] 0.02961719 0.02884375 0.02807031 0.02729688 0.02652344 0.02497656

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

## [1] 0.02497656

Model 5

##  [1] 0.03039063 0.02575000 0.02265625 0.01956250 0.01801563 0.01724219
##  [7] 0.01646875 0.01492188 0.01492188 0.01414844 0.01414844 0.01105469

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

## [1] 0.01105469