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Leduc, Guillaume; Zeng, Xiangchen

Convergence rate of regime-switching trees. (English) Zbl 1358.41009

J. Comput. Appl. Math. 319, 56-76 (2017).
Summary: Considering a general class of regime-switching geometric random walks and a broad class of piecewise twice differentiable payoff functions, we show that convergence of option prices occurs at a speed of order \(\mathcal{O}(n^{- \beta})\), where \(\beta = 1/2\) when the payoff is discontinuous and \(\beta = 1\) otherwise.

Cited in 3 Documents

MSC:

41A25 Rate of convergence, degree of approximation
65C50 Other computational problems in probability (MSC2010)
65C20 Probabilistic models, generic numerical methods in probability and statistics

Keywords:

regime-switching Black-Scholes; discretization; rate of convergence
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\textit{G. Leduc} and \textit{X. Zeng}, J. Comput. Appl. Math. 319, 56--76 (2017; Zbl 1358.41009)
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References:

[1] Zhu, S. P.; Badran, A.; Lu, X., A new exact solution for pricing European options in a two-state regime-switching economy, Comput. Math. Appl., 64, 8, 2744-2755, (2012) · Zbl 1268.91170
[2] Liu, R. H., A new tree method for pricing financial derivatives in a regime-switching mean-reverting model, Nonlinear Anal. RWA, 13, 6, 2609-2621, (2012) · Zbl 1254.91726
[3] 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
[4] Buffington, J.; Elliott, R. J., American options with regime switching, Int. J. Theor. Appl. Finance, 5, 05, 497-514, (2002) · Zbl 1107.91325
[5] Fuh, C. D.; Ho, K. W.R.; Hu, I.; Wang, R. H., Option pricing with Markov switching, J. Data Sci., 10, 3, 483-509, (2012)
[6] Guo, X., Information and option pricings, Quant. Finance, 1, 1, 38-44, (2001)
[7] Hardy, Mary R., A regime-switching model of long-term stock returns, N. Am. Actuar. J., 5, 2, 41-53, (2001) · Zbl 1083.62530
[8] Hardy, Mary, Investment guarantees: modeling and risk management for equity-linked life insurance, vol. 215, (2003), John Wiley & Sons · Zbl 1092.91042
[9] Li, M. Y.L.; Lin, H. W.W., Examining the volatility of Taiwan stock index returns via a three-volatility-regime Markov-switching arch model, Rev. Quant. Finance Account., 21, 2, 123-139, (2003)
[10] Hobbes, G.; Lam, F.; Loudon, G. F., Regime shifts in the stock-bond relation in Australia, Rev. Pac. Basin Financ. Markets Policies, 10, 01, 81-99, (2007)
[11] Nishina, K.; Maghrebi, N.; Holmes, M. J., Nonlinear adjustments of volatility expectations to forecast errors: evidence from Markov-regime switches in implied volatility, Rev. Pac. Basin Financ. Markets Policies, 15, 03, (2012)
[12] Costabile, M.; Leccadito, A.; Massabó, I.; Russo, E., A reduced lattice model for option pricing under regime-switching, Rev. Quant. Finance Account., 42, 4, 667-690, (2014)
[13] Bollen, N. P.B., Valuing options in regime-switching models, J. Derivatives, 6, 1, 38-49, (1998)
[14] Khaliq, A. Q.M.; Liu, R. H., New numerical scheme for pricing American option with regime-switching, Int. J. Theor. Appl. Finance, 12, 03, 319-340, (2009) · Zbl 1204.91127
[15] Liu, R. H., Regime-switching recombining tree for option pricing, Int. J. Theor. Appl. Finance, 13, 03, 479-499, (2010) · Zbl 1233.91284
[16] Yuen, F. L.; Yang, H., Option pricing with regime switching by trinomial tree method, J. Comput. Appl. Math., 233, 8, 1821-1833, (2010) · Zbl 1181.91315
[17] J.H. Yoon, U.J. Choi, B.H. Lim, B.G. Jang, A lattice method for lookback options with regime-switching volatility, Available at SSRN 1523634 (2011).
[18] Yuen, F. L.; Siu, T. K.; Yang, H., Option valuation by a self-exciting threshold binomial model, Math. Comput. Modelling, 58, 1, 28-37, (2013) · Zbl 1297.91139
[19] Liu, R. H.; Nguyen, D., A tree approach to options pricing under regime-switching jump diffusion models, Int. J. Comput. Math., 92, 12, 2575-2595, (2015) · Zbl 1335.91106
[20] Ma, J.; Zhu, T., Convergence rates of trinomial tree methods for option pricing under regime-switching models, Appl. Math. Lett., 39, 13-18, (2015) · Zbl 1320.91158
[21] J. Ma, T. Zhu, Erratum to “convergence rates of trinomial tree methods for option pricing under regime-switching models”, available at ResearchGate 268631955 (2015). · Zbl 1320.91158
[22] Leduc, G., Option convergence rate with geometric random walks approximations, Stoch. Anal. Appl., 34, 5, 767-791, (2016) · Zbl 1410.91456
[23] Naik, V., Option valuation and hedging strategies with jumps in the volatility of asset returns, J. Finance, 48, 5, 1969-1984, (1993)
[24] Leduc, G., A European option general first-order error formula, ANZIAM J., 54, 4, 248-272, (2013) · Zbl 1282.91337
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.