Static approach and SD fees - Cont

With this exercise the fair fee for VAs with GMAB and GMDB riders will be found by means of the static approach. The caracteristics of the contracts are the following:

• Contract expires at T = 10 years
• Age of the policyholder at contract inception in 60
• Both GMAB and GMDB pay the minimum amount as the roll-up of premium.
• The roll-up rate is 1%
• The fee is state-dependent with base fee 6%
• The initial state-dependent barrier is the GMAB minimum amount at T = 10 indicated with G

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

##  [1] 0.07750000 0.05781250 0.04656250 0.04093750 0.03812500 0.03390625
##  [7] 0.03250000 0.03109375 0.02968750 0.02828125 0.02828125 0.02406250

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

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

##  [1] 0.06906250 0.04937500 0.03953125 0.03390625 0.03109375 0.02828125
##  [7] 0.02687500 0.02546875 0.02546875 0.02406250 0.02406250 0.02265625

Eventually the financial and mortality models will be the one published in BBM2010. In this case the age at contract inception is 40.

##  [1] 0.04656250 0.03390625 0.02687500 0.02265625 0.02125000 0.01843750
##  [7] 0.01703125 0.01703125 0.01562500 0.01562500 0.01492188 0.01281250