An extended CEV model and the Legendre transform-dual-asymptotic solutions for annuity contracts
This paper develops an extended constant elasticity of variance (E-CEV) model to overcome the shortcomings of the general CEV model. Under the E-CEV model, we study the optimal investment strategy before and after retirement in a defined contribution pension plan where benefits are paid by annuity. By applying the Legendre transform, dual theory and an asymptotic expansion approach, we respectively derive two asymptotic strategies for a CRRA and CARA utility functions in two different periods. Furthermore, we find that each asymptotic strategy can be decomposed into an optimal zero-order strategy and a perturbation strategy. The optimal zero-order strategy denotes an investment strategy where the current volatility is just equal to the mean level of the volatility, whereas the perturbation strategy provides an approximation solution to hedge the slow varying nature of the current volatility deviating from mean level. Finally, we find that the optimal zero-order strategy under given conditions will reduce to the results of Devolder etÂ al. (2003), Xiao etÂ al. (2007) and Gao (2009), respectively.
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- Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
- Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
- Boulier, Jean-Francois & Huang, ShaoJuan & Taillard, Gregory, 2001. "Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 173-189, April.
- Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
- Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002.
"Alternative Models for Stock Price Dynamics,"
CIRANO Working Papers
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Xiao, Jianwu & Hong, Zhai & Qin, Chenglin, 2007. "The constant elasticity of variance (CEV) model and the Legendre transform-dual solution for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 302-310, March.
- Devolder, Pierre & Bosch Princep, Manuela & Dominguez Fabian, Inmaculada, 2003. "Stochastic optimal control of annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 227-238, October.
- Gerrard, Russell & Haberman, Steven & Vigna, Elena, 2004. "Optimal investment choices post-retirement in a defined contribution pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 321-342, October.
- Branger, Nicole & Schlag, Christian & Schneider, Eva, 2008. "Optimal portfolios when volatility can jump," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1087-1097, June.
- Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
- Beckers, Stan, 1980. " The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-73, June.
- Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2004. "Optimal design of the guarantee for defined contribution funds," Journal of Economic Dynamics and Control, Elsevier, vol. 28(11), pages 2239-2260, October.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 1999.
"Transform Analysis and Asset Pricing for Affine Jump-Diffusions,"
NBER Working Papers
7105, National Bureau of Economic Research, Inc.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
- Gao, Jianwei, 2009. "Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 9-18, August.
- Munk, Claus & Sorensen, Carsten & Nygaard Vinther, Tina, 2004. "Dynamic asset allocation under mean-reverting returns, stochastic interest rates, and inflation uncertainty: Are popular recommendations consistent with rational behavior?," International Review of Economics & Finance, Elsevier, vol. 13(2), pages 141-166.
- Emms, P. & Haberman, S. & Savoulli, I., 2007. "Optimal strategies for pricing general insurance," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 15-34, January.
- Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997.
"Empirical Performance of Alternative Option Pricing Models,"
Yale School of Management Working Papers
ysm65, Yale School of Management.
- Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
- Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
- Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-19, March.
- Steven Haberman & Elena Vigna, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," ICER Working Papers - Applied Mathematics Series 09-2002, ICER - International Centre for Economic Research.
- Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2004. "Optimal design of the guarantee for defined contribution funds," ULB Institutional Repository 2013/7602, ULB -- Universite Libre de Bruxelles.
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