Static and mixed approach with SD fees

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 varies from 6% to 18%
• The state-dependent barrier is the GMAB minimum amount at T = 5
• The surrender penalty is 2% constant.

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

The regression is LSMC is done only when the GMAB guarantee is in the money

## Static

##  [1] 108.8831 108.0425 107.2474 106.4125 105.6032 104.8565 104.1774
##  [8] 103.5036 102.8894 102.2664 101.6757 101.2125 100.7154

## Mixed

##  [1] 108.8506 107.9861 107.1047 106.2655 105.4512 104.5715 103.8396
##  [8] 103.1932 102.5616 101.9721 101.4704 100.9520 100.4951

We’re going to repeat it changing the GBM and the constant interest rate with the financial and mortality model published in BMOP2011.

## Static

##  [1] 106.95856 105.78651 104.68925 103.64823 102.65653 101.74984 100.95252
##  [8] 100.22801  99.56414  98.95897  98.47383  98.05356  97.70449

## Mixed

##  [1] 106.80541 105.59238 104.40007 103.23504 102.24276 101.25702 100.53033
##  [8] 100.05012  99.70697  99.41129  99.14908  98.96065  98.73241

Eventually the financial and mortality models will be the one published in BBM2010. In this case the age at contract inception is 40. Even in this case, the regression in LSMC is done only when the GMAB guarantee is in the money.

## Static

##  [1] 103.83006 102.54902 101.27873 100.02596  98.81341  97.62609  96.51341
##  [8]  95.45224  94.47975  93.57812  92.77930  92.03978  91.36860

## Mixed

##  [1] 103.67084 102.27994 100.77335  99.34632  98.15605  97.59459  97.14693
##  [8]  96.77200  96.52702  96.28434  96.02887  95.77415  95.54709