Fig 4.5 with model 3 (volatility of K is 0.3) and model 2

With this exercise VAs with GMAB and GMDB riders are priced by means of the 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.
• We’re going to calculate the contract value with model 3 where sigma_K is now 0.3 and model 2 with constant volatility 0.2

The regression in LSMC is done only when the account is below the barrier.

## Model 3 with sigma_K = 0.3:

##  [1] 116.13280 112.20706 108.05370 103.91206 100.99207  99.69601  98.94585
##  [8]  98.41775  97.94912  97.55171  97.21638  96.90319  96.62990

## Model 2:

##  [1] 118.46456 114.86219 111.10389 107.48260 104.17168 101.98873 100.43415
##  [8]  99.51520  98.73770  98.22206  97.72584  97.34234  96.98410