×

A bivariate model for evaluating equity-linked policies with surrender option. (English) Zbl 1401.91128

Summary: This article proposes a bivariate lattice model for evaluating equity-linked policies embedding a surrender option when the underlying equity dynamics is described by a geometric Brownian motion with stochastic interest rate. The main advantage of the model stays in that the original processes for the reference fund and the interest rate are directly discretized by means of lattice approximations, without resorting to any additional transformation. Then, the arising lattices are combined in order to establish a bivariate tree where equity-linked policy premiums are computed by discounting the policy payoff over the lattice branches, and allowing early exercise at each premium payment date to model the surrender decision.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G20 Derivative securities (option pricing, hedging, etc.)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
62P05 Applications of statistics to actuarial sciences and financial mathematics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aase, K. K. & Persson, S. A. (1994). Pricing of unit-linked life insurance policies. Scandinavian Actuarial Journal1, 26-52. · Zbl 0814.62067
[2] Bacinello, A. R. (2005). Endogenous model of surrender conditions in equity-linked life insurance. Insurance: Mathematics and Economics37(2), 270-296. · Zbl 1118.91054
[3] Bacinello, A. R., Biffis, E. & Millossovich, P. (2009). Pricing life insurance contracts with early exercise features. Journal of Computational and Applied Mathematics233(1), 27-35. · Zbl 1179.91098
[4] Bacinello, A. R., Biffis, E. & Millossovich, P. (2010). Regression-based algorithms for life insurance contracts with surrender guarantees. Quantitative Finance10(9), 1077-1090. · Zbl 1210.91056
[5] Bacinello, A. R. & Ortu, F. (1993). Pricing equity-linked life insurance with endogenous minimum guarantees. Insurance: Mathematics and Economics12(3), 245-257. · Zbl 0778.62093
[6] Bacinello, A. R. & Ortu, F. (1994). Single and periodic premiums for guaranteed equity-linked life insurance under interest-rate risk: the ‘Lognormal+Vasicek’ case. In L. Peccati & M. Viren, (Eds.), Financial modeling, pp. 1-25. Heidelberg: Physica-Verlag.
[7] Boyle, P. & Schwartz, E. (1977). Equilibrium pricing of guarantees under equity-linked contracts. Journal of Risk and Insurance44(4), 639-660.
[8] Brennan, M. J. & Schwartz, E. S. (1976). The pricing of equity-linked life insurance policies with an asset value guarantee. Journal of Financial Economics3(3), 195-213.
[9] Costabile, M., Gaudenzi, M., Massabó, I. & Zanette, A. (2009). Evaluating fair premiums of equity-linked policies with surrender option in a bivariate model. Insurance: Mathematics and Economics45(2), 286-295. · Zbl 1231.91167
[10] Costabile, M. & Massabó, I. (2010). A simplified approach to approximate diffusion processes widely used in finance. Journal of Derivatives17(3), 65-85.
[11] Costabile, M., Massabó, I. & Russo, E. (2008). A binomial model for valuing equity-linked policies embedding surrender options. Insurance: Mathematics and Economics42(3), 873-886. · Zbl 1141.91496
[12] Cox, J. C., Ingersoll, J. & Ross, S. (1985). A theory of the term structure of interest rates. Econometrica53, 385-407. · Zbl 1274.91447
[13] Delbaen, F. (1990). Equity linked policy. Bulletin Association Royale Actuaires Belges84, 33-52.
[14] Gaudenzi, M., Lepellere, M. A. & Zanette, A. (2010). The singular points binomial method for pricing American path-dependent options. Journal of Computational Finance14(1), 29-56. · Zbl 1284.91571
[15] Nielsen, J. A. & Sandmann, K. (1995). Equity-linked life insurance: A model with stochastic interest rates. Insurance: Mathematics and Economics16(3), 225-253. · Zbl 0872.62094
[16] Ronkainen, V., Koskinen, L. & Berglund, R. (2007). Topical modelling issues in Solvency II. Scandinavian Actuarial Journal2, 135-146. · Zbl 1164.62086
[17] Wey, J. Z. (1996). Valuing American equity options with a stochastic interest rate: a note. Journal of Financial Engineering2(2), 195-206.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.