Pricing maturity guarantee with dynamic withdrawal benefit
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
- Gerber, Hans U. & Shiu, Elias S. W., 1999. "From ruin theory to pricing reset guarantees and perpetual put options," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 3-14, March.
- Leung, Kwai Sun & Kwok, Yue Kuen & Leung, Seng Yuen, 2008. "Finite-time dividend-ruin models," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 154-162, February.
- Lee, Hangsuck, 2003. "Pricing equity-indexed annuities with path-dependent options," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 677-690, December.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.