Adjusted mixed approach with constant fee
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 constant.
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. In this case, at each step the linear regression in LSMC will be done only for paths where the GMAB guarantee is out of the money.
## Fee: 0.06
## Static: 99.95477
## Mixed: 102.586
## Fee: 0.07
## Static: 98.69378
## Mixed: 101.8006
## Fee: 0.08
## Static: 97.72466
## Mixed: 101.1322
## Fee: 0.09
## Static: 96.96334
## Mixed: 100.5331
## Fee: 0.1
## Static: 96.40756
## Mixed: 99.94588
## Fee: 0.11
## Static: 95.99733
## Mixed: 99.42404
## Fee: 0.12
## Static: 95.70805
## Mixed: 98.92146
## Fee: 0.13
## Static: 95.52057
## Mixed: 98.46575
## Fee: 0.14
## Static: 95.37941
## Mixed: 98.07901
## Fee: 0.15
## Static: 95.29325
## Mixed: 97.71793
## Fee: 0.16
## Static: 95.24124
## Mixed: 97.4244
## Fee: 0.17
## Static: 95.22218
## Mixed: 97.1501
## Fee: 0.18
## Static: 95.20298
## Mixed: 96.90856