×

zbMATH — the first resource for mathematics

Pricing dynamic fund protections for a hyperexponential jump diffusion process. (English) Zbl 1386.91148
Summary: This article deals with the valuation of dynamic fund protections (DFPs) under a jump diffusion model, where the jump size follows a hyperexponential distribution. The closed-form solution of the value of DFP is obtained in terms of Laplace transform. A numerical example is provided to show that the explicit solution is easy to implement by using the Gaver-Stehfest algorithm. Effects of key parameters are analyzed at last. The valuation method developed in this work can be used in pricing various variable annuities and path-dependent financial products.

MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
60G51 Processes with independent increments; Lévy processes
60J75 Jump processes (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cai, N. 2009. On the first passage time of a hyper-exponential jump diffusion process. Operation Research Letters 37(2):127-34. · Zbl 1163.60039
[2] Cai, N., N. Chen, and X. Wan. 2009. Pricing double barrier options under a flexible jump diffusion model. Operation Research Letters 37(3):163-7. · Zbl 1187.91208
[3] Cai, N., and S. G. Kou. 2012. Pricing Asian options under a hyper-exponential jump diffusion model. Operations Research 60(1):64-77. · Zbl 1241.91111
[4] Chang, C. C., Y. H. Lian, and M. H. Tsay. 2012. Pricing dynamic guaranteed funds under a double exponential jump diffusion model. Academia Economic Papers 40(2):269-306.
[5] Chu, C. C., and Y. K. Kwok. 2004. Reset and withdrawal rights in dynamic fund protection. Insurance: Mathematics and Economics 34(2):273-95. · Zbl 1136.91421
[6] Fung, H. K., and L. K. Li. 2003. Pricing discrete dynamic fund protections. North American Actuarial Journal 7(4):23-31. · Zbl 1084.91506
[7] Gerber, H. U., and G. Pafumi. 2000. Pricing dynamic investment fund protection. North American Actuarial Journal 4(2):28-37. · Zbl 1083.91516
[8] Gerber, H. U., and E. S. Shiu. 1998. Pricing perpetual options for jump processes. North American Actuarial Journal 2(3):101-7. · Zbl 1081.91528
[9] Gerber, H. U., and E. S. Shiu. 1999. From ruin theory to pricing reset guarantees and perpetual put options. Insurance: Mathematics and Economics 24(1):3-14. · Zbl 0939.91065
[10] Gerber, H. U., and E. S. Shiu. 2003. Pricing perpetual fund protection with withdrawal option. North American Actuarial Journal 7(2):60-77. · Zbl 1084.60512
[11] Gerber, H. U., E. S. Shiu, and H. Yang. 2013. Valuing equity-linked death benefits in jump diffusion models. Insurance: Mathematics and Economics 53(3):615-23. · Zbl 1290.91162
[12] Imai, J., and P. P. Boyle. 2001. Dynamic fund protection. North American Actuarial Journal 5(3):31-47. · Zbl 1083.60513
[13] Kou, S. G. 2002. A jump-diffusion model for option pricing. Management Science 48:1086-101. · Zbl 1216.91039
[14] Kou, S. G., and H. Wang. 2003. First passage times of a jump diffusion process. Advances in Applied Probability 35:504-31. · Zbl 1037.60073
[15] Siu, C. C., S. C. P. Yam, and H. Yang. 2015. Valuing equity-linked death benefits in a regime-switching framework. ASTIN Bulletin 45(02):355-95. · Zbl 1390.91211
[16] Tse, W. M., E. C. Chang, L. K. Li, and H. M. Mok. 2008. Pricing and hedging of discrete dynamic guaranteed funds. Journal of Risk and Insurance 75(1):167-92.
[17] Wong, H. Y. 2007. Analytical valuation of dynamic fund protection under CEV. WSEAS Transactions on Mathematics 6(2):324-9.
[18] Wong, H. Y., and C. M. Chan. 2007. Lookback options and dynamic fund protection under multiscale stochastic volatility. Insurance: Mathematics and Economics 40(3):357-85. · Zbl 1183.91173
[19] Wong, H. Y., and K. W. Lam. 2009. Valuation of discrete dynamic fund protection under Lévy processes. North American Actuarial Journal 13(2):202-16.
[20] Yin, C. C., Y. Shen, and Y. Z. Wei. 2013. Exit problems for jump processes with applications to dividend problems. Journal of Computational and Applied Mathematics 245:30-52. · Zbl 1267.91076
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.