×

Semi-static hedging for GMWB in variable annuities. (English) Zbl 1291.91205

Summary: The Guaranteed Minimum Withdrawal Benefit (GMWB) is an option embedded in a variable annuity that guarantees the policyholder to get the initial investment back by making periodic withdrawals regardless of the impact of poor market performance. In the paper we discuss methods of pricing and hedging of some versions of GMWBs. In particular we develop a method of constructing semi-static hedging strategies that offer several advantages over dynamic hedging. The idea is to first find the closest path-independent option to the guarantee, or its liability part, and then to construct a portfolio of traded European options that approximates the optimal option. This strategy requires fewer portfolio adjustments than delta hedging and outperforms the latter when there are random jumps in the underlying price. We illustrate the proposed method with numerical examples.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91B30 Risk theory, insurance (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bowie J., Risk 7 pp 45– (1994)
[2] Boyle P. P., Journal of Financial Economics 8 pp 259– (1980)
[3] Boyle P. P., Insurance: Mathematics and Economics 42 pp 189– (2008) · Zbl 1141.91421
[4] Breeden D. T., Journal of Business 51 pp 621– (1978)
[5] Carr P., Risk Magazine 10 pp 139– (1997)
[6] Carr P., Journal of Finance 53 (3) pp 1165– (1998)
[7] Carr P., Volatility pp 417– (1998)
[8] Carr P., Static Hedging of Standard Options (2004)
[9] Coleman T. F., Insurance: Mathematics and Economics 38 pp 215– (2006) · Zbl 1128.91020
[10] Cont R., Financial Modelling with Jump Processes (2004) · Zbl 1052.91043
[11] Föllmer H., ASTIN Bulletin 18 pp 147– (1988)
[12] Föllmer H., Contributions to Mathematical Economics pp 205– (1986)
[13] Glasserman P., Monte Carlo Methods in Financial Engineering (2004) · Zbl 1038.91045
[14] Karlin S., A Second Course in Stochastic Processes (1981) · Zbl 0469.60001
[15] Kou S. G., Management Science 50 (9) pp 1178– (2004)
[16] Liu Y., Pricing and Hedging the Guaranteed Minimum Withdrawal Benefits in Variable Annuities (2010)
[17] Milevsky A., Insurance: Mathematics and Economics 38 pp 21– (2006) · Zbl 1116.91048
[18] Møller T., North American Actuarial Journal 5 (2) pp 79– (2001) · Zbl 1083.91546
[19] Pelsser A., Insurance: Mathematics and Economics 33 pp 283– (2003) · Zbl 1103.91352
[20] Schweizer M., Mathematics of Operations Research 20 pp 1– (1995) · Zbl 0835.90008
[21] Schweizer M., Option Pricing, Interest Rates and Risk Management pp 538– (1999)
[22] Takahashi A., Journal of Futures Markets 29 (1) pp 1– (2009)
[23] Toft K. B., Journal of Financial and Quantitative Analysis 31 pp 233– (1996)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.