Connection between trinomial trees and finite difference methods for option pricing with state-dependent switching rates

References

• J. Ahn and M. Song, Convergence of the trinomial tree method for pricing European/American options, Appl. Math. Comput. 189 (2007), pp. 575–582.
   Web of Science ®Google Scholar
• D.D. Aingworth, S.R. Das, and R. Motwani, A simple approach for pricing equity options with Markov switching state variables, Quant. Fin. 6 (2006), pp. 95–105.
   Web of Science ®Google Scholar
• R. Bansal and H. Zhou, Term structure of interest rates with regime shifts, J. Fin. 57 (2002), pp. 1997–2043.
   Web of Science ®Google Scholar
• A. Bensaïda, The frequency of regime switching in financial market volatility, J. Emp. Fin. 32 (2015), pp. 63–79.
   Web of Science ®Google Scholar
• N.P.B. Bollen, Valuing options in regime-switching models, J. Deriv. 6 (1998), pp. 38–49.
   Google Scholar
• P. Boyle, Option valuation using a three-jump process, Int. Opt. J. 3 (1986), pp. 7–12.
   Google Scholar
• P. Boyle and T. Draviam, Pricing exotic options under regime switching, Ins. Math. Econ. 40 (2007), pp. 267–282.
   Web of Science ®Google Scholar
• J. Buffington and R.J. Elliott, American options with regime switching, Int. J. Theor. Appl. Fin. 5 (2002), pp. 497–514.
   Google Scholar
• R.J. Elliot, V. Krishnamurthy, and J. Sass, Moment based regression algorithms for the drift and volatility estimation in continuous-time Markov switching models, Econometr. J. 11 (2008), pp. 244–270.
   Web of Science ®Google Scholar
• P. Eloe, R.H. Liu, and J.Y. Sun, Double barrier option under regime-switching exponential mean-reverting process, Int. J. Comput. Math. 86 (2009), pp. 964–981.
   Web of Science ®Google Scholar
• P. Eloe, R.H. Liu, M. Yatsuki, G. Yin, and Q. Zhang, Optimal selling rules in a regime-switching exponential Gaussian diffusion model, SIAM J. Appl. Math. 69 (2008), pp. 810–829.
   Web of Science ®Google Scholar
• I. Florescu, R.H. Liu, M.C. Mariani, and G. Sewell, Numerical schemes for option pricing in regime-switching jump diffusion models, Int. J. Theor. Appl. Fin. 16 (2013), pp. 1–25.
   Google Scholar
• X. Guo, Information and option pricings, Quant. Fin. 1 (2000), pp. 38–44.
   Google Scholar
• X. Guo and Q. Zhang, Closed-form solutions for perpetual American put options with regime switching, SIAM J. Appl. Math. 64 (2004), pp. 2034–2049.
   Web of Science ®Google Scholar
• M. Hahn, S. Frühwirth-Schnatter, and J. Sass, Markov chain Monte Carlo methods for parameter estimation in multidimensional continuous time Markov switching models, J. Fin. Econometr. 8 (2010), pp. 88–121.
   Web of Science ®Google Scholar
• J.D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica 57 (1989), pp. 357–384.
   Web of Science ®Google Scholar
• M.R. Hardy, A regime-switching model for long-term stock returns, Nor. Am. Actuar. J. 5 (2001), pp. 41–53.
   Google Scholar
• J.X. Jiang, R.H. Liu, and D. Nguyen, A recombining tree method for option pricing with state-dependent switching rates, Int. J. Theor. Appl. Fin. 19 (2016), pp. 1650012. (26 pages).
   Web of Science ®Google Scholar
• L. Jiang, Mathematical Modeling and Methods for Option Pricing, World Scientific, River Edge, NJ, 2005.
   Google Scholar
• A.Q.M. Khaliq and R.H. Liu, New numerical scheme for pricing American option with regime-switching, Int. J. Theor. Appl. Fin. 12 (2009), pp. 319–340.
   Google Scholar
• Y.K. Kwok, Mathematical Models of Financial Derivatives, Springer-Verlag, Singapore, 1998.
   Google Scholar
• O.A. Ladyzenskaja, V.A. Solonnikov, and N.N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type. Translated from the Russian by S. Smith, Translations of Mathematical Monographs. Vol. 23, American Mathematical Society, Providence, R.I., 1968.
   Google Scholar
• C. Landén, Bond pricing in a hidden Markov model of the short rate, Fin. Stochast. 4 (2000), pp. 371–389.
   Google Scholar
• R.H. Liu, Regime-switching recombining tree for option pricing, Int. J. Theor. Appl. Fin. 13 (2010), pp. 479–499.
   Google Scholar
• R.H. Liu, A new tree method for pricing financial derivatives in a regime-switching mean-reverting model, Nonlinear Anal. Real World Appl. 13 (2012), pp. 2609–2621.
   Web of Science ®Google Scholar
• R.H. Liu and J.L. Zhao, A lattice method for option pricing with two underlying assets in the regime-switching model, J. Comput. Appl. Math. 250 (2013), pp. 96–106.
   Web of Science ®Google Scholar
• J. Ma and T. Zhu, Convergence rate of trinomial tree methods for option pricing under regime-switching models, Appl. Math. Lett. 39 (2015), pp. 13–18.
   Web of Science ®Google Scholar
• C. Rey, S. Rey, and J.R. Viala, Detection of high and low states in the stock market returns with MCMC method in a Markov switching model, Econ. Modell. 41 (2014), pp. 145–155.
   Web of Science ®Google Scholar
• M. Rubinstein, On the relation between binomial and trinomial option pricing models, J. Deriv. 8 (2000), pp. 47–50.
   Google Scholar
• J.W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer-Verlag, New York, 1995.
   Google Scholar
• Y. Tian, A modified lattice approach to option pricing, J. Fut. Mark. 13 (1993), pp. 563–577.
   Web of Science ®Google Scholar
• D.D. Yao, Q. Zhang, and X.Y. Zhou, in H.M. Yan, G. Yin, and Q. Zhang (eds.), A regime-switching model for European options, in Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems Springer, New York, 2006, pp. 281–300.
   Google Scholar
• G. Yin, R.H. Liu, and Q. Zhang, Recursive algorithms for stock liquidation: A stochastic optimization approach, SIAM J. Control Optim. 13 (2002), pp. 240–263.
   Web of Science ®Google Scholar
• G. Yin, Q. Zhang, F. Liu, R.H. Liu, and Y. Cheng, Stock liquidation via stochastic approximation using NASDAQ daily and intra-day data, Math. Fin. 16 (2006), pp. 217–236.
   Web of Science ®Google Scholar
• F. Yuen and H. Yang, Option pricing with regime switching by trinomial tree method, J. Comput. Appl. Math. 233 (2010), pp. 1821–1833.
   Web of Science ®Google Scholar
• F. Yuen and H. Yang, Pricing Asian options and equity-indexed annuities with regime switching by the trinomial tree method, Nor. Am. Actuar. J. 14 (2010), pp. 256–277.
   Google Scholar
• Q. Zhang, Stock trading: An optimal selling rule, SIAM J. Control Optim. 40 (2001), pp. 64–87.
   Web of Science ®Google Scholar
• Q. Zhang, G. Yin, and R.H. Liu, A near-optimal selling rule for a two-time-scale market model, SIAM Journal of Multiscale Modeling & Simulation 4 (2005), pp. 172–193.
   Web of Science ®Google Scholar
• X. Zhou and G. Yin, Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (2003), pp. 1466–1482.
   Web of Science ®Google Scholar