Fig 4.5 five models - No adjust

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.
Five models are used.

The regression in LSMC is always done regardless the account is below the barrier.

Model 1

## Static

##  [1] 118.19312 114.63443 111.22851 107.89413 104.89865 102.36032 100.00718
##  [8]  97.99603  96.19086  94.54963  93.29906  92.13427  91.21370

## Mixed

##  [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

Model 2

## Static

##  [1] 117.89225 114.13612 110.71792 107.40206 104.43474 101.78774  99.36845
##  [8]  97.28298  95.43406  93.89860  92.55540  91.55051  90.63784

## Mixed

##  [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

Model 3

## Static

##  [1] 115.79795 111.75395 107.64960 103.80739 100.33742  97.08665  94.33931
##  [8]  92.05490  90.28862  89.04351  88.07200  87.44620  87.04128

## Mixed

##  [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

Model 4

## Static

##  [1] 116.51161 112.18708 108.09524 103.99712 100.39516  97.06704  94.29839
##  [8]  91.96623  90.28536  88.93853  88.03569  87.47076  87.13424

## Mixed

##  [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

Model 5

## Static

##  [1] 109.04128 104.56245  99.94011  95.55400  91.09600  86.87239  82.63733
##  [8]  78.90783  75.65482  72.96513  70.83567  69.05030  67.75434

## Mixed

##  [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