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Valuation of equity-indexed annuity under jump diffusion process. (English) Zbl 1199.91094
Summary: The equity-indexed annuity (EIA) contract offers a proportional participation in the return on a specified equity index, in addition to a guaranteed return on the single premium. In general, in valuation of equity-indexed annuity, it is often assumed that the equity index is within the Black-Scholes framework, but some rare events (release of an unexpected economic figure, major political changes or even a natural disaster in a major economy) can lead to brusque variations in prices. So in the present work we study the equity index following a jump diffusion process. By Esscher transform, we obtain a closed form of the valuation of point-to-point EIA, which can be expressed as a function of some pricing factors. Finally, we conduct several numerical experiments in which the break even participation rate \(\alpha\) can be solved when the other factors are fixed. The relationship between \(\alpha\) and the other factors are also discussed.
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics