Mathematical and Statistical Methods for Actuarial Sciences and Finance

292 F. Quittard-Pinon and R. Randrianarivony

30 35 40 45 50 55 60 65 70 75

0

20

40

60

80

100

120

Mortality impact −− USA

Age (years)

Insurance risk charge (bp)

No jumps (flat)

Kou (flat)

Kou, Gompertz (stoch.)

Kou, Makeham (stoch.)

Fig. 1.Annual risk insurance charge in basis points, USA

are introduced. In this case, fees are notably higher. Second, the choice of mortality
model does not have a significant impact.

5 Conclusions

To analyse the effects of jump risk, stochastic interest rate and mortality on GMDBs,
this paper assumes a particular jump diffusion process, namely a Kou process, for the
return of the policyholder subaccount and a Vasicek term structure of interest rate,
while the mortality is of a Gompertz or a Makeham type. The contract fair value is
obtained using a methodology based on generalised Fourier analysis. It is shown that
the largest impact among the three risk factors on the GMDB fees is due to stochastic
interest rate. Jumps and mortality have smaller influence. The fair insurance risk
charges are found to be significantly higher than Milevsky and Posner [8] reported,
but still below the fees required by insurance companies.