CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2008, 24(6) 648-659 DOI:      ISSN: 1001-4268 CN: 31-1256

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Valuation of Equity-Indexed Annuity under Jump Diffusion Process

Qian Linyi, Zhu Liping, Yao Dingjun

School of Finance and Statistics, East China Normal University

Abstract��

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, valuation of Equity-Indexed Annuity 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.

Keywords�� Equity-indexed annuities   Esscher transform   participation rate   point to point   jump diffusion process.
Received 1900-01-01 Revised 1900-01-01 Online:
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