Fig 4.9
With this exercise VAs with GMAB and GMDB riders are priced by means of the static amd mixed approaches. The caracteristics of the contracts are the following:
- Contract expires at T = 15 years
- Age of the policyholder at contract inception is 50
- Both GMAB and GMDB pay the minimum amount as the roll-up of premium.
- The roll-up rates are 0% and 2%
- The fee is both CST and SD with the base fee which varies from 1% to 13%
- The state-dependent barrier is the GMAB minimum amount at T = 15
- The surrender penalty is 2% constant.
With regards to the simulation:
- The number of Monte Carlo simulations will be 20000.
- It is considered just model4
We’re going to compare the values calculated by using the mixed approach and static approach when the fee is CST and when it’s SD. The mixed approach is always adjusted.
Mixed with SD and CST fee roll-up 0% and 2%
## Mixed - SD - Roll-up 0%
## [1] 108.82800 106.90749 104.39946 100.78144 98.88819 98.34786 98.13219
## [8] 97.85743 97.73948 97.55473 97.34815 97.14176 96.91010
## Mixed - CST - Roll-up 0%
## [1] 101.69883 98.65083 97.81761 97.31723 96.98551 96.72170 96.44488
## [8] 96.20300 95.95365 95.70643 95.46990 95.23224 95.00333
## Mixed - SD - Roll-up 2%
## [1] 116.51756 112.17846 107.71933 103.40841 100.54646 99.28632 98.62670
## [8] 98.14616 97.75196 97.40414 97.08686 96.80613 96.54134
## Mixed - CST - Roll-up 2%
## [1] 111.38356 106.50248 103.35745 101.30815 99.97760 99.14139 98.57639
## [8] 98.11480 97.72625 97.38931 97.08367 96.79960 96.53445
SD fees Roll-up 0%
## Static
## [1] 108.85979 106.88054 104.81215 102.70719 100.56166 98.61074 96.58926
## [8] 94.79138 92.90806 91.25298 89.74190 88.33626 87.22116
## Mixed
## [1] 108.82800 106.90749 104.39946 100.78144 98.88819 98.34786 98.13219
## [8] 97.85743 97.73948 97.55473 97.34815 97.14176 96.91010
CST fees Roll-up 0%
## Static
## [1] 99.17435 89.75976 82.23804 76.56504 72.36620 69.29264 67.20845
## [8] 65.88870 65.06673 64.60638 64.32840 64.22812 64.16651
## Mixed
## [1] 101.69883 98.65083 97.81761 97.31723 96.98551 96.72170 96.44488
## [8] 96.20300 95.95365 95.70643 95.46990 95.23224 95.00333
Roll-up 0% previuos two graphs combined
SD fees Roll-up 2%
## Static
## [1] 116.60661 112.24689 108.08135 104.10823 100.33845 97.02507 94.25382
## [8] 91.98500 90.25644 88.91246 88.03701 87.48906 87.11236
## Mixed
## [1] 116.51756 112.17846 107.71933 103.40841 100.54646 99.28632 98.62670
## [8] 98.14616 97.75196 97.40414 97.08686 96.80613 96.54134
CST fees Roll-up 2%
## Static
## [1] 110.73597 103.08906 97.32806 93.24823 90.45131 88.61562 87.52291
## [8] 86.87115 86.55415 86.40796 86.32695 86.29328 86.28525
## Mixed
## [1] 111.38356 106.50248 103.35745 101.30815 99.97760 99.14139 98.57639
## [8] 98.11480 97.72625 97.38931 97.08367 96.79960 96.53445
Roll-up 2% previuos two graphs combined
