Static and mixed approach with SD fees while increasing the barrier

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 = 5 years
• Age of the policyholder at contract inception is 60
• 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 is 8%
• The initial state-dependent barrier is the GMAB minimum amount at T = 5 indicated with G
• The surrender penalty is 2% constant.

We are going to progressively increase the barrier with the formula (1 + k) * G where k varies from -0.5 to 0 with step 0.1

With regards to the simulation:

• The number of Monte Carlo simulations will be 20000.
• Constant interest rate r = 0.03
• Underlying fund is a GBM with volatility 0.2
• Intensity of mortality is given by the Weibull mortality function with c1=90.43, c2=10.36

In the mixed approach, the regression is done only when the GMAB guarantee is in the money

##          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]      [,7]
## [1,] 114.7068 114.6340 114.3617 113.1871 110.5154 107.1139  99.51823
## [2,] 114.7072 114.6537 114.3073 113.2378 110.5023 107.1221 100.39202

In the graph the dashed line corresponds to the constant fee case.