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SECTION B

Pricing American options under multi-state regime switching with an efficient L- stable method

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Pages 2530-2550 | Received 24 Jan 2015, Accepted 10 Jun 2015, Published online: 02 Sep 2015

References

  • U.M. Ascher, S.J. Ruuth, and B.T.R. Wetton, Implicit–explicit methods for time-dependent partial differential equations, SIAM J. Numer. Anal. 32(3) (1995), pp. 797–823. doi: 10.1137/0732037
  • U.M. Ascher, S.J. Ruuth, and R.J. Spiteri, Implicit-explicit Runge–Kutta methods for time-dependent partial differential equations, Appl. Numer. Math. 25 (1997), pp. 151–167. doi: 10.1016/S0168-9274(97)00056-1
  • R. Bansal and H. Zhou, Term structure of interest rates with regime shifts, J. Finance 57(5) (2002), pp. 1997–2043. doi: 10.1111/0022-1082.00487
  • G. Beylkin, J.M. Keiser, and L. Vozovoi, A new class of time discretization schemes for the solution of nonlinear PDEs, J. Comput. Phys. 147 (1998), pp. 362–387. doi: 10.1006/jcph.1998.6093
  • S. Boyarchenko and S. Levendorskii, American options in regime-switching models, SIAM J. Control Optim. 48 (2009), pp. 1353–1376. doi: 10.1137/070682897
  • P. Boyle and T. Draviam, Pricing exotic options under regime switching, Insurance Math. Econom. 40 (2007), pp. 267–282. doi: 10.1016/j.insmatheco.2006.05.001
  • J. Buffington and R.J. Elliott, American options with regime switching, Int. J. Theor. Appl. Finance 5 (2002), pp. 497–514. doi: 10.1142/S0219024902001523
  • Z. Chen and P.A. Forsyth, Implications of a regime switching model on natural gas storage valuation and optimal operation, Quant. Finance 10 (2010), pp. 159–176. doi: 10.1080/14697680802374791
  • S.M. Cox and P.C. Matthews, Exponential time differencing for stiff systems, J. Comput. Phys. 176(2) (2002), pp. 430–455. doi: 10.1006/jcph.2002.6995
  • R.J. Elliott, L. Chan, and T.K. Siu, Option pricing and Esscher transform under regime switching, Ann. Finance 1 (2005), pp. 423–432. doi: 10.1007/s10436-005-0013-z
  • F.X. Giraldo, J.F. Kelly, and E.M. Constantinescu, Implicit-explicit formulations of a three dimensional nonhydrostatic unified model of the atmosphere, SIAM J. Sci. Comput. 35(5) (2013), pp. B1162–B1194. doi: 10.1137/120876034
  • E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer-Verlag, Berlin, 1991.
  • M.R. Hardy, A regime-switching model for long-term stock returns, N. Am. Actuar. J. 5 (2001), pp. 41–53. doi: 10.1080/10920277.2001.10595984
  • A.D. Holmes, H. Yang, and S. Zhang, A front-fixing finite element method for the valuation of American options with regime switching, Int. J. Comput. Math. 89 (2012), pp. 1094–1111. doi: 10.1080/00207160.2012.663911
  • S.D. Howison, C. Reisinger, and J.H. Witte, The effect of nonsmooth payoffs on the penalty approximation of American options, SIAM J. Financ. Math. 4 (2013), pp. 539–574. doi: 10.1137/12087743X
  • Y. Huang, P.A. Forsyth, and G. Labahn, Methods for pricing American options under regime switching, SIAM J. Sci. Comput. 33(5) (2011), pp. 2144–2168. doi: 10.1137/110820920
  • W. Hundsdorfer and J.G. Verwer, Numerical Solution of Time-dependent Advection–Diffusion–Reaction Equations, Springer-Verlag, Berlin, Heidelberg, 2003.
  • S. Ikonen, Efficient numerical solution of Black–Scholes equation by finite difference method, Licentiate thesis, Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland, 2003.
  • P. Jaeckel, Finite differencing schemes as Padé approximants, 2013. Available at http://www.pjaeckel.webspace.virginmedia.com/FiniteDifferencingSchemesAsPad.
  • A.Q.M. Khaliq and R.H. Liu, New numerical scheme for pricing American option with regime-switching, Int. J. Theor. Appl. Finance 12 (2009), pp. 319–340. doi: 10.1142/S0219024909005245
  • A.Q.M. Khaliq, B. Kleefeld, and R.H. Liu, Solving complex PDE systems for pricing American options with regime-switching by efficient exponential time differencing schemes, Numer. Methods Partial Differential Equations 29(1) (2013), pp. 320–336. doi: 10.1002/num.21714
  • B. Kleefeld, A.Q.M. Khaliq, and B.A. Wade, An ETD Crank–Nicolson method for reaction–diffusion systems, Numer. Methods Partial Differential Equations 28 (2012), pp. 1309–1335. doi: 10.1002/num.20682
  • R.H. Liu, Regime-switching recombining tree for option pricing, Int. J. Theor. Appl. Finance 13(3) (2010), pp. 479–499. doi: 10.1142/S0219024910005863
  • R.H. Liu and J.L. Zhaob, A lattice method for option pricing with two underlying assets in the regime-switching model, J. Comput. Appl. Math. 250 (2013), pp. 96–106. doi: 10.1016/j.cam.2013.02.012
  • J. Ma and T. Zhu, Convergence rates of trinomial tree methods for option pricing under regime-switching models, Appl. Math. Lett. 39 (2015), pp. 13–18. doi: 10.1016/j.aml.2014.07.020
  • C. Moler and C. Van Loan, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev. 45(1) (2003), pp. 3–49. doi: 10.1137/S00361445024180
  • B.F. Nielsen, O. Skavhaug, and A. Tveito, Penalty and front-fixing methods for the numerical solution of American option problems, J. Comput. Finance 5 (2002), pp. 69–97.
  • D. Qiang and Z. Wenxiang, Analysis and applications of the exponential time differencing schemes and their contour integration modifications, BIT Numer. Math. 55 (2005), pp. 307–328.
  • S. Salmi, J. Toivanen, and L. von Sydow, An IMEX-scheme for pricing options under stochastic volatility models with jumps, SIAM J. Sci. Comput. 36(5) (2014), pp. B817–B834. doi: 10.1137/130924905
  • H. Yang, A numerical analysis of American options with regime switching, J. Sci. Comput. 44 (2010), pp. 69–91. doi: 10.1007/s10915-010-9365-2
  • G. Yin and Q. Zhang, Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Springer-Verlag New York, Inc., New York, NY, 1998.
  • M. Yousuf, A.Q.M. Khaliq, and B. Kleefeld, The numerical approximation of nonlinear Black–Scholes model for exotic path-dependent American options with transaction cost, Int. J. Comput. Math. 89 (2012), pp. 1239–1254. doi: 10.1080/00207160.2012.688115
  • F.L. Yuen and H. Yang, Option pricing with regime switching by trinomial tree method, J. Comput. Appl. Math. 233 (2010), pp. 1821–1833. doi: 10.1016/j.cam.2009.09.019
  • K. Zhang, K.L. Teo, and M. Swartz, A robust numerical scheme for pricing American options under regime switching based on penalty method, J. Comput. Econ. 43(4) (2014), pp. 463–483. DOI: 10.1007/s10614-013-9361-3.
  • R. Zvan, P.A. Forsyth, and K.R. Vetzal, Penalty methods for American options with stochastic volatility, J. Comput. Appl. Math. 91 (1998), pp. 199–218. doi: 10.1016/S0377-0427(98)00037-5

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