In-the-Money test

In the following example we’re going to price VA contracts with GMAB and GMDB riders with the following features:

• Expiry T = 5 (years).
• The initial single premium is 100.
• The guaranteed minimum for both GMAB and GMDB is the roll up of premium with rate 2%.
• The contract fees are state-dependent.
• The state-dependent barrier is set to be the roll-up of premium at time T= 5 (years).

Contract values corresponding to a base fee ranging from 6% to 12% will be estimated by means of both the static and mixed approaches. The number of Monte Carlo simulations will be 20000. The models for the underlying fun, interest rate and intensity of mortality is the one used in BMOP2011.

With this test, at each step the linear regression in LSMC will be done only for paths where the GMAB guarantee is in-the-money.

## Fee:  0.06 
## Static: 107.0676 
## Mixed:  107.0378 
## Fee:  0.07 
## Static: 105.9582 
## Mixed:  105.8167 
## Fee:  0.08 
## Static: 104.927 
## Mixed:  104.5923 
## Fee:  0.09 
## Static: 103.8408 
## Mixed:  103.4794 
## Fee:  0.1 
## Static: 102.8543 
## Mixed:  102.3547 
## Fee:  0.11 
## Static: 101.9374 
## Mixed:  101.3644 
## Fee:  0.12 
## Static: 101.0722 
## Mixed:  100.4783 
## Fee:  0.13 
## Static: 100.311 
## Mixed:  100.0016 
## Fee:  0.14 
## Static: 99.65805 
## Mixed:  99.67538 
## Fee:  0.15 
## Static: 99.09503 
## Mixed:  99.36964 
## Fee:  0.16 
## Static: 98.56413 
## Mixed:  99.10345 
## Fee:  0.17 
## Static: 98.11156 
## Mixed:  98.90833 
## Fee:  0.18 
## Static: 97.73941 
## Mixed:  98.72886

Conclusions

Doing the regression just when the guarantee is in-the-money gets really closer to the static values. However we’re still below most of the times, so it seems to not improve that much the behavior of the mixed approach with state-dependent fees. In addition, it lacks interpretability and empirical evidence.