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 is 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.

## SD

##  [1] 116.49612 112.20470 107.99470 104.02520 100.38695  97.05166  94.25762
##  [8]  91.97383  90.24547  88.93893  88.02258  87.45640  87.12125

## CST

##  [1] 110.75419 103.03027  97.31165  93.24492  90.41471  88.61328  87.53048
##  [8]  86.87185  86.55183  86.39238  86.32378  86.29993  86.29686