Lundi 08 Mars 15H30 - 16 H 30
Donatien HAINAUT (ESC Rennes)
"Optimal design of profit sharing rate by FFT"
Le séminaire aura lieu en salle S018 de 15 H 30 à 16 H 30
In this talk, we will discuss an application of the Fourier Transform to price life insurance liabilities.
After a brief review of the notion of Fourier Transform, we investigate how this tool can help us to calculate a fair profit sharing rate for participating policies with a minimum interest rate guaranteed. In the scheme studied, the bonus credited to policies depends on the performance of a basket of two assets: a stock and a zero coupon bond and on the guarantee. The dynamics of the instantaneous short rates is driven by a Hull and White model. While the stocks follow a double exponential jump-diffusion model. The participation level is determined such that the return retained by the insurer is sufficient to hedge the interest rate guarantee. Given that the return of the total asset is not lognormal, we rely on a Fast Fourier Transform to compute the fair value of bonus and guarantee options. As showed in an example, our approach allows us to emphasize the link between the investment policy and the fair profit sharing rate.
This research comes from the paper: “Optimal design of profit sharing rates by FFT”, accepted for publication in Insurance: Mathematics & economics (forthcoming in 2010).
Prochaine séance : Le jeudi 08 Avril de 16 H 15 à 18 H 30