Fig4.8

With this exercise VAs with GMAB and GMDB riders are priced by means of the mixed 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 rate considered is 2%
• The fee is state-dependent and the base fee varies from 4% to 6%
• The state-dependent barrier is the GMAB minimum amount at T = 15
• Penalties vary from 0% to 10%

With regards to the simulation:

• The number of Monte Carlo simulations will be 20000.
• The Weibull function was fitted to the 2015 Italian life table and the estimated parameters are c1=88.14778, c2=10.002.

##          [,1]     [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
## [1,] 103.5476 103.3781 103.20501 103.40695 103.47749 103.61302 103.83831
## [2,] 101.6806 101.1127 100.45942 100.04910  99.80864  99.69938  99.76037
## [3,] 100.8075 100.0077  99.27399  98.59367  97.94642  97.53985  96.97005
##           [,8]      [,9]     [,10]     [,11]
## [1,] 103.89739 103.96062 104.00991 103.99926
## [2,]  99.86337  99.80171  99.97507 100.16596
## [3,]  96.74471  96.51546  96.59976  96.63747