Convergence rates of trinomial tree methods for option pricing under regime-switching models. (English) Zbl 1320.91158

Summary: Recently trinomial tree methods have been developed to option pricing under regime-switching models. Although these novel trinomial tree methods are shown to be accurate via numerical examples, it needs to give a rigorous proof of the accuracy which can theoretically guarantee the reliability of the computations. The aim of this paper is to prove the convergence rates (measure of the accuracy) of the trinomial tree methods for the option pricing under regime-switching models.


91G60 Numerical methods (including Monte Carlo methods)
91G20 Derivative securities (option pricing, hedging, etc.)
Full Text: DOI


[1] Hamilton, J. D., A new approach to the economic analysis of nonstationary time series and the business cycle, Ecomometrica, 57, 357-384, (1989) · Zbl 0685.62092
[2] Aingworth, D. D.; Das, S. R.; Motwani, R., A simple approach for pricing equity options with Markov switching state variables, Quant. Finance, 6, 95-105, (2006) · Zbl 1136.91410
[3] Bollen, N. P.B., Valuing options in regime-switching models, J. Derivatives, 6, 38-49, (1998)
[4] Boyle, P.; Draviam, T., Pricing exotic options under regime switching, Insurance Math. Econom., 40, 267-282, (2007) · Zbl 1141.91420
[5] Buffington, J.; Elliott, R. J., American options with regime switching, Int. J. Theor. Appl. Finance, 5, 497-514, (2002) · Zbl 1107.91325
[6] Eloe, P.; Liu, R. H.; Sun, J. Y., Double barrier option under regime-switching exponential mean-reverting process, Int. J. Comput. Math., 86, 964-981, (2009) · Zbl 1163.91393
[7] Guo, X., Information and option pricings, Quant. Finance, 1, 38-44, (2000)
[8] Guo, X.; Zhang, Q., Closed-form solutions for perpetual American put options with regime switching, SIAM J. Appl. Math., 64, 2034-2049, (2004) · Zbl 1061.90082
[9] Hardy, M. R., A regime-switching model for long-term stock returns, North American Actuar. J., 5, 41-53, (2001) · Zbl 1083.62530
[10] Khaliq, A. Q.M.; Liu, R. H., New numerical scheme for pricing American option with regime-switching, Int. J. Theor. Appl. Finance, 12, 319-340, (2009) · Zbl 1204.91127
[11] Liu, R. H., Regime-switching recombining tree for option pricing, Int. J. Theor. Appl. Finance, 13, 479-499, (2010) · Zbl 1233.91284
[12] Liu, R. H.; Zhao, J. L., A lattice method for option pricing with two underlying assets in the regime-switching model, J. Comput. Appl. Math., 250, 96-106, (2013) · Zbl 1285.91143
[13] Yao, D. D.; Zhang, Q.; Zhou, X. Y., A regime-switching model for European options, in stochastic processes, optimization, and control theory, (Yan, H. M.; Yin, G.; Zhang, Q., Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, (2006), Springer), 281-300 · Zbl 1136.91015
[14] Yuen, F.; Yang, H., Option pricing with regime switching by trinomial tree method, J. Comput. Appl. Math., 233, 1821-1833, (2010) · Zbl 1181.91315
[15] Yuen, F.; Yang, H., Pricing Asian options and equity-indexed annuites with regime switching by the trinomial tree method, North American Actuar. J., 14, 256-277, (2010) · Zbl 1219.91145
[16] Bansal, R.; Zhou, H., Term structure of interest rates with regime shifts, J. Finance, 57, 1997-2043, (2002)
[17] Landén, C., Bond pricing in a hidden Markov model of the short rate, Finance Stoch., 4, 371-389, (2000) · Zbl 1016.91046
[18] Liu, R. H., A new tree method for pricing financial derivatives in a regime-switching mean-reverting model, Nonlinear Analysis RWA, 13, 2609-2621, (2012) · Zbl 1254.91726
[19] Zhou, X.; Yin, G., Markowitz’s mean-variance portfolio selection with regime switching: a continuous-time model, SIAM J. Control Optim., 42, 1466-1482, (2003) · Zbl 1175.91169
[20] Eloe, P.; Liu, R. H.; Yatsuki, M.; Yin, G.; Zhang, Q., Optimal selling rules in a regime-switching exponential Gaussian diffusion model, SIAM J. Appl. Math., 69, 810-829, (2008) · Zbl 1175.91079
[21] Yin, G.; Liu, R. H.; Zhang, Q., Recursive algorithms for stock liquidation: a stochastic optimization approach, SIAM J. Control Optim., 13, 240-263, (2002) · Zbl 1021.91022
[22] Yin, G.; Zhang, Q.; Liu, F.; Liu, R. H.; Cheng, Y., Stock liquidation via stochastic approximation using NASDAQ daily and intra-day data, Math. Finance, 16, 217-236, (2006) · Zbl 1128.91031
[23] Zhang, Q., Stock trading: an optimal selling rule, SIAM J. Control Optim., 40, 64-87, (2001) · Zbl 0990.91014
[24] Zhang, Q.; Yin, G.; Liu, R. H., A near-optimal selling rule for a two-time-scale market model, SIAM J. Multiscale Mode. Simul., 4, 172-193, (2005) · Zbl 1108.91031
[25] Boyle, P., Option valuation using a three-jump process, Int. Options J., 3, 7-12, (1986)
[26] Tian, Y., A modified lattice approach to option pricing, J. Futures Markets, 13, 563-577, (1993)
[27] Rubinstein, M., On the relation between binomial and trinomial option pricing models, J. Derivatives, 8, 47-50, (2000)
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.