Willow tree algorithms for pricing Guaranteed Minimum Withdrawal Benefits under jump-diffusion and CEV models

References

• Alonso-García, J., Wood, O. and Ziveyi, J., Pricing and hedging guaranteed minimum withdrawal benefits under a general Lévy framework using the COS method. Quant. Finance, 2018, 18(6), 1049–1075. doi: 10.1080/14697688.2017.1357832
   Web of Science ®Google Scholar
• Azimzadeh, P. and Forsyth, P.A., The existence of optimal bang-bang controls for GMxB contracts. SIAM J. Financ. Math., 2015, 6(1), 117–139. doi: 10.1137/140953885
   Google Scholar
• Bacinello, A.R., Millossovich, P. and Montealegre, A., The valuation of GMWB variable annuities under alternative fund distributions and policyholder behaviours. Scand. Actuar. J., 2016, 2016(5), 446–465. doi: 10.1080/03461238.2014.954608
   Web of Science ®Google Scholar
• Ballotta, L. and Kyriakou, I., Convertible bond valuation in a jump diffusion setting with stochastic interest rates. Quant. Finance, 2015, 15, 115–129. doi: 10.1080/14697688.2014.935464
   Web of Science ®Google Scholar
• Bauer, D., Kling, A. and Russ, J., A universal pricing framework for guaranteed minimum benefits in variable annuities. Astin Bull., 2008, 38, 621–651. doi: 10.1017/S0515036100015312
   Web of Science ®Google Scholar
• Chen, Z., Vetzal, K. and Forsyth, P., The effect of modeling parameters on the value of GMWB guarantees. Insur. Math. Econ., 2008, 43, 165–173. doi: 10.1016/j.insmatheco.2008.04.003
   Web of Science ®Google Scholar
• Costabile, M., A lattice-based model to evaluate variable annuities with guaranteed minimum withdrawal benefits under a regime-switching model. Scand. Actuar. J., 2017, 2017(3), 231–244.
   Web of Science ®Google Scholar
• Cox, J., Notes on option pricing I: Constant elasticity of diffusions. Working paper, Stanford University, 1975.
   Google Scholar
• Cox, J., Ingersoll, J. and Ross, S., A theory of the term structure of interest rates. Econometrica, 1985, 53(2), 385–407. doi: 10.2307/1911242
   Web of Science ®Google Scholar
• Curran, M., Willow power: Optimizing derivative pricing trees. Algo Res. Q., 2001, 4, 15–24.
   Google Scholar
• Dai, M., Kwok, Y.K. and Zong, J., Guaranteed minimum withdrawal benefit in variable annuities. Math. Financ., 2008, 18, 595–611. doi: 10.1111/j.1467-9965.2008.00349.x
   Web of Science ®Google Scholar
• Forsyth, P. and Vetzal, K., An optimal stochastic control framework for determining the cost of hedging of variable annuities. J. Econ. Dyn. Control, 2014, 44, 29–53. doi: 10.1016/j.jedc.2014.04.005
   Web of Science ®Google Scholar
• Geman, H. and Shih, Y.F., Modeling commodity prices under the CEV model. JAI, 2009, 11, 65–84. doi: 10.3905/JAI.2009.11.3.065
   Google Scholar
• Gudkov, N., Ignatieva, K. and Ziveyi, J., Pricing of GMWB options in variable annuities under stochastic volatility, stochastic interest rates and stochastic mortality via the componentwise splitting method. To appear in Quantitative Finance, 2018.
   Google Scholar
• Hill, I. and Holder, R., Algorithm as 99: Fitting Johnson curves by moments. Appl. Stat., 1976, 25, 180–189. doi: 10.2307/2346692
   Google Scholar
• Huang, Y.Q. and Forsyth, P.A., Analysis of a penalty method for pricing a guaranteed minimum withdrawal benefit (GMWB). J. Numer. Anal., 2012, 32, 320–351. doi: 10.1093/imanum/drq044
   Google Scholar
• Huang, Y.Q., Forsyth, P.A. and Labahn, G., Iterative methods for the solution of a singular control formulation of a GMWB pricing problem. Numerische Mathematik, 2012, 122, 133–167. doi: 10.1007/s00211-012-0455-y
   Web of Science ®Google Scholar
• Huang, Y.T. and Kwok, Y.K., Analysis of optimal withdrawal policies in withdrawal guarantee products. J. Econ. Dyn. Control, 2014, 45, 320–351. doi: 10.1016/j.jedc.2014.05.008
   Web of Science ®Google Scholar
• Ignatieva, K., Song, A. and Ziveyi, J., Pricing and hedging of guaranteed minimum benefits under regime-switching and stochastic mortality. Insur. Math. Econ., 2016, 70, 286–300. doi: 10.1016/j.insmatheco.2016.06.014
   Web of Science ®Google Scholar
• Johnson, N., System of frequency curves generated by methods of translation. Biometrika, 1949, 36, 149–176. doi: 10.1093/biomet/36.1-2.149
   PubMed Web of Science ®Google Scholar
• Kang, B. and Ziveyi, J., Optimal surrender of guaranteed minimum maturing benefits under stochastic volatility and interest rates. Insur. Math. Econ., 2018, 79, 43–56. doi: 10.1016/j.insmatheco.2017.12.012
   Web of Science ®Google Scholar
• Lu, L. and Xu, W., A simple and efficient two-factor willow tree method for convertible bond pricing with stochastic interest rate and default risk. J. Derivatives, 2017, 25, 37–54. doi: 10.3905/jod.2017.25.1.037
   Web of Science ®Google Scholar
• Lu, L., Xu, W. and Qian, Z., Efficient convergent lattice method for Asian options pricing with superlinear complexity. J. Comput. Financ., 2017, 20, 1–38.
   Web of Science ®Google Scholar
• Luo, X. and Shevchenko, P.V., Valuation of variable annuities with guaranteed minimum withdrawal and death benefits via stochastic control optimization. Insur. Math. Econ., 2015, 62, 5–15. doi: 10.1016/j.insmatheco.2015.02.003
   Web of Science ®Google Scholar
• Merton, R.C., Option pricing when underlying stock returns are discontinuous. J. Financ. Econ., 1976, 3, 125–144. doi: 10.1016/0304-405X(76)90022-2
   Web of Science ®Google Scholar
• Milevsky, M. and Salisbury, T., Financial valuation of guaranteed minimum withdrawal benefits. Insur. Math. Econ., 2006, 38, 21–38. doi: 10.1016/j.insmatheco.2005.06.012
   Web of Science ®Google Scholar
• Moenig, T. and Bauer, D., Revisiting the risk-neutral approach to optimal policyholder behavior: A study of withdrawal guarantees in variable annuities. Working paper in the 12th Symposium on Finance, Banking, and Insurance, Germany, 2011.
   Google Scholar
• Peng, J.J., Leung, K.S. and Kwok, Y.K., Pricing guaranteed minimum withdrawal benefits under stochastic interest rates. Quant. Finance, 2012, 12(6), 933–941. doi: 10.1080/14697680903436606
   Web of Science ®Google Scholar
• Shevchenko, P.V. and Luo, X.L., Valuation of variable annuities with guaranteed minimum withdrawal benefit under stochastic interest rate. Working paper, Macquarie University, 2017.
   Google Scholar
• Wang, G. and Xu, W., A unified willow tree framework for one-factor short rate models. J. Derivatives, 2018, 25, 33–54. doi: 10.3905/jod.2018.1.064
   Web of Science ®Google Scholar
• Xu, W., Hong, Z. and Qin, C., A new sampling strategy willow tree method with application to path-dependent option pricing. Quant. Finance, 2013, 13, 861–872. doi: 10.1080/14697688.2012.762111
   Web of Science ®Google Scholar
• Xu, W. and Yin, Y., Pricing American options by willow tree method under jump-diffusion process. J. Derivatives, 2014, 22, 1–9. doi: 10.3905/jod.2014.22.1.046
   Web of Science ®Google Scholar
• Yang, S.S. and Dai, T.S., A flexible tree for evaluating guaranteed minimum withdrawal benefits under deferred life annuity contracts with various provisions. Insur. Math. Econ., 2013, 52, 231–242. doi: 10.1016/j.insmatheco.2012.12.005
   Web of Science ®Google Scholar
• Yao, Y., Xu, W. and Kwok, Y.K., Willow tree algorithms for pricing exotic derivatives on discrete realized variance under time-changed Lévy process. Working paper, Tongji University, 2019.
   Google Scholar