Calibration of CIR to life table

We’re going to calibrate both a Gompertz model and the stochastic CIR model to the HMD IT 1x10 table (2010-2019) for a 65 years old man.

Here follows the survival function implied by the table.

Let’s fit a Gompertz model:

## theta =  0.1176776  mu0 =  0.009089793

Let’s calibrate the CIR model to the same survival function

## alpha =  1e-04  theta =  0.1211644  sigma =  0.01  mu0 =  0.008319741

Monte Carlo is used to estimate the residual life time. Finally we plot some simulated paths out of the calibrated CIR model along with the fitted Gompertz intesity.

## Expected residual life =  19.13459