Journal article
Pricing maturity guarantee with dynamic withdrawal benefit
Insurance, mathematics & economics, Vol.47(2), pp.216-223
2010
DOI: 10.1016/j.insmatheco.2010.04.006
Abstract
Motivated by the importance of withdrawal benefits for enhancing sales of variable annuities, we propose a new equity-linked product which provides a dynamic withdrawal benefit (DWB) during the contract period and a minimum guarantee at contract maturity. The term DWB is coined to reflect the duality between it and dynamic fund protection. Under the Black–Scholes framework and using results pertaining to reflected Brownian motion, we obtain explicit pricing formulas for the DWB payment stream and the maturity guarantee. These pricing formulas are also derived by means of Esscher transforms, which is another seminal contribution by Gerber to finance. In particular, we show that there are closed-form formulas for pricing European put and call options on a traded asset whose price can be modeled as the exponential of a reflected Brownian motion.
Details
- Title: Subtitle
- Pricing maturity guarantee with dynamic withdrawal benefit
- Creators
- Bangwon Ko - Department of Statistics and Actuarial Science, Soongsil University, Seoul, South KoreaElias S W Shiu - Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242-1409, USALi Wei - School of Finance, Renmin University of China, Beijing 100872, PR China
- Resource Type
- Journal article
- Publication Details
- Insurance, mathematics & economics, Vol.47(2), pp.216-223
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.insmatheco.2010.04.006
- ISSN
- 0167-6687
- eISSN
- 1873-5959
- Language
- English
- Date published
- 2010
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9983985989202771
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