Fig 4.5 comparison

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 is 2%
• The fee is state-dependent and the base fee 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.
• All five models

We’re going to compare the values calculated by using the mixed approach with and without the adjustment of doing the regression only when the account is below the barrier.

## Static

##  [1] 118.30462 114.74733 111.12661 107.80459 105.06002 102.37904 100.06229
##  [8]  98.03278  96.20914  94.62853  93.31506  92.15651  91.22904

## Mixed

##  [1] 118.29896 114.57175 110.98637 107.44333 104.47863 102.04794 100.00123
##  [8]  99.17303  98.56284  98.02105  97.61553  97.22785  96.89115

## Mixed without adjust

##  [1] 113.97167 111.11951 108.10104 105.39320 103.10609 101.43866 100.02496
##  [8]  99.15361  98.52078  97.97475  97.56134  97.16649  96.80115

## Static

##  [1] 117.87242 114.27479 110.69818 107.34033 104.35757 101.63903  99.32587
##  [8]  97.22381  95.42908  93.89109  92.56596  91.49942  90.60476

## Mixed

##  [1] 117.87865 114.26159 110.60353 106.99826 103.83184 101.54781 100.31721
##  [8]  99.49192  98.72630  98.19011  97.69836  97.29845  96.95941

## Mixed without adjust

##  [1] 117.03539 113.00184 109.41521 106.05987 103.35978 101.43053 100.24046
##  [8]  99.35321  98.66615  98.12921  97.68164  97.24874  96.89524

## Static

##  [1] 115.84145 111.71738 107.66951 103.79463 100.28341  97.15415  94.36024
##  [8]  92.06244  90.27261  89.02348  88.09694  87.48199  87.04237

## Mixed

##  [1] 115.81122 111.66584 107.20921 102.88666 100.35447  99.27880  98.66416
##  [8]  98.19462  97.81216  97.45555  97.13774  96.85757  96.57357

## Mixed without adjust

##  [1] 114.37403 109.76022 105.70046 102.19543 100.30490  99.27486  98.63820
##  [8]  98.17235  97.78040  97.42959  97.12716  96.84643  96.57923

## Static

##  [1] 116.52166 112.32804 108.03912 103.97856 100.37778  97.03874  94.28933
##  [8]  91.97336  90.25592  88.94217  88.03807  87.46482  87.11837

## Mixed

##  [1] 116.53467 112.21362 107.65487 103.39323 100.49667  99.26690  98.64034
##  [8]  98.15877  97.75170  97.39979  97.09532  96.80764  96.54690

## Mixed without adjust

##  [1] 115.26038 110.59879 106.40009 102.56835 100.44424  99.29675  98.65317
##  [8]  98.13050  97.73706  97.38518  97.08699  96.80666  96.54811

## Static

##  [1] 108.86499 104.54153  99.95298  95.60841  91.06080  86.72960  82.65471
##  [8]  78.95187  75.68187  72.93319  70.76831  69.10815  67.68259

## Mixed

##  [1] 109.05406 104.56972  99.29021  97.61095  97.02472  96.71000  96.42817
##  [8]  96.16662  95.92530  95.67685  95.43591  95.19882  94.96598

## Mixed without adjust

##  [1] 107.86934 102.56973  98.46482  97.55033  96.99207  96.70938  96.43489
##  [8]  96.16908  95.91832  95.67437  95.44549  95.20124  94.96480