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.
• Model 4 is used for the financial and mortality.

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] 115.93477 111.72233 107.56683 103.59567  99.96320  96.76929  93.97920
##  [8]  91.81163  90.13616  88.87519  88.08249  87.56808  87.09637

## Mixed

##  [1] 115.81173 111.70091 107.27577 102.85993 100.38101  99.31218  98.71283
##  [8]  98.23979  97.84017  97.49004  97.17559  96.88833  96.61396

## Mixed without adjust

##  [1] 114.98229 110.43283 106.15401 102.32617 100.39713  99.36320  98.67067
##  [8]  98.21857  97.83348  97.48489  97.18165  96.88180  96.62089

With model 3:

## Static

##  [1] 115.89198 111.71213 107.59605 103.68725  99.99754  96.68248  93.95735
##  [8]  91.78598  90.17765  88.88636  88.08881  87.55387  87.12385

## Mixed

##  [1] 115.84745 111.70538 107.35007 102.95427 100.34199  99.31472  98.70759
##  [8]  98.23347  97.82229  97.48821  97.17136  96.88292  96.61672

## Mixed without adjust

##  [1] 114.83475 110.46262 106.10375 102.43060 100.38586  99.36095  98.67328
##  [8]  98.19841  97.81006  97.47874  97.16910  96.87683  96.61825

With model 2:

## Static

##  [1] 117.43317 113.61335 110.25755 107.10002 104.09094 101.39869  99.07233
##  [8]  97.00798  95.22128  93.62569  92.47694  91.45714  90.63107

## Mixed

##  [1] 117.42672 113.63813 110.17579 106.74585 103.73115 101.66623 100.44417
##  [8]  99.53151  98.76129  98.16661  97.70323  97.26731  96.92808

## Mixed without adjust

##  [1] 117.03459 113.10754 109.36519 106.00591 103.43679 101.66280 100.38890
##  [8]  99.29536  98.60110  98.02092  97.58489  97.18113  96.82110

With model 1:

## Static

##  [1] 117.61789 113.91555 110.55525 107.29506 104.26874 101.64033  99.34948
##  [8]  97.34290  95.58565  94.06395  92.75378  91.51923  90.67779

## Mixed

##  [1] 117.44932 113.91505 110.26747 106.76913 103.65375 101.36372 100.34782
##  [8]  99.31435  98.54109  97.95155  97.51690  97.17281  96.76403

## Mixed without adjust

##  [1] 113.77661 111.21336 108.20582 105.54151 103.06590 101.40104 100.16693
##  [8]  99.22321  98.43582  97.92140  97.50206  97.06591  96.74455