Fig4.3 - CST vs STD

With this exercise VAs with GMAB and GMDB riders are priced 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 rates considered are 0%, 1% and 2%
• The fee is both state-dependent and constant and the base fee varies from 1% to 13%
• The state-dependent barrier is the GMAB minimum amount at T = 15

With regards to the simulation:

• The number of Monte Carlo simulations will be 20000.
• Underlying fund, interest rate, volatility and intensity of mortality follow the dynamics given by the systems of SDEs in BMOP2011.
• The Weibull function was fitted to the 2015 Italian life table and the estimated parameters are c1=88.14778, c2=10.002.
  This model will be referred to as model 4.

##          [,1]     [,2]     [,3]     [,4]      [,5]     [,6]     [,7]
## [1,] 108.0920 106.1908 104.0818 101.9802 100.02773 97.96692 95.93010
## [2,] 111.0162 107.7457 104.2747 100.8923  97.46436 94.09816 90.98326
## [3,] 115.9348 111.7223 107.5668 103.5957  99.96320 96.76929 93.97920
##          [,8]     [,9]    [,10]    [,11]    [,12]    [,13]
## [1,] 94.12606 92.38329 90.75499 89.31288 88.14248 86.82726
## [2,] 88.06379 85.41612 83.37203 81.64641 80.16610 79.03239
## [3,] 91.81163 90.13616 88.87519 88.08249 87.56808 87.09637

##           [,1]      [,2]     [,3]     [,4]     [,5]     [,6]     [,7]
## [1,]  98.55695  89.24788 81.98043 76.37775 72.22589 69.22742 67.15468
## [2,] 103.55604  95.05205 88.49570 83.71432 80.19058 77.82072 76.36703
## [3,] 110.19980 102.68914 97.03852 92.97375 90.24677 88.47771 87.43824
##          [,8]     [,9]    [,10]    [,11]    [,12]    [,13]
## [1,] 65.92137 65.11764 64.63836 64.49654 64.34841 64.29717
## [2,] 75.45051 74.94580 74.69448 74.54981 74.48442 74.47247
## [3,] 86.87813 86.59124 86.43494 86.36669 86.36261 86.32107