Abstract
Guo (Methodol Comput Appl Probab 3(2):135–143, 2001a) derived the Laplace transform of the first-passage time in a 2-state Markov-switching model and gave one of the pioneering works improving the analytical tractability of Markov-switching models. However, the Laplace transforms in her paper are wrong. This short note provides the correct expression and an alternative proof using the matrix Wiener–Hopf technique.
Similar content being viewed by others
References
Asmussen S (1995) Stationary distributions for fluid flow models with or without Brownian noise. Commun Statist Stoch Models 11(1):21–49
Barlow M, Rogers L, Williams D (1990) Wiener–Hopf factorization for matrices. Lect Notes Math 784:324–331
Boyle P, Draviam T (2007) Pricing exotic options under regime switching. Insur Math Econ 40:267–282
Buffington J, Elliott RJ (2002) American options with regime switching. Int J Theor Appl Financ 5:497–514
Elliott RJ, Chan L, Siu TK (2005) Option pricing and Esscher transform under regime switching. Ann Finance 1(4):423–432
Eloe P, Liu R, Sun J (2009) Double barrier option under regime-switching exponential mean-reverting process. Int J Comput Math 86(6):964–981
Guo X (1999) Inside information and stock fluctuation. PhD thesis, Rutgers University, New Yersey
Guo X (2001a) When the “Bull” meets the “Bear”—a first passage time problem for a hidden Markov process. Methodol Comput Appl Probab 3(2):135–143
Guo X (2001b) An explicit solution to an optimal stopping problem with regime switching. J Appl Probab 38:464–481
Guo X (2004) Closed-form solutions for perpetual American put options with regime switching. SIAM J Appl Math 64(6):2034–2049
Henriksen PN (2011) Pricing barrier options by a regime switching model. J Quant Financ 11(8):1221–1231
Hieber P (2012) First-passage times of regime switching models. Working paper
Hieber P, Scherer M (2010) Efficiently pricing barrier options in a Markov-switching framework. J Comput Appl Math 235:679–685
Jiang Z, Pistorius M (2008) On perpetual American put valuation and first-passage in a regime-switching model with jumps. Finance Stochast 12(3):331–355
Jobert A, Rogers, L (2006) Option pricing with Markov modulated dynamics. SIAM J Control Optim 44:2063–2078
Khaliq A (2010) New numerical scheme for pricing American option with regime-switching. J Theor Appl Financ 12(3):319–340
Kim M, Jang B-G, Lee H-S (2008) A first-passage-time model under regime-switching market environment. J Bank Financ 32:2617–2627
Kudryavtsev O (2010) Efficient pricing options under regime switching. Working paper
London R, McKean H, Rogers L, Williams D (1982) A martingale approach to some Wiener–Hopf problems. Lect Notes Math 920:68–90
Metwally S, Atiya A (2002) Using Brownian bridge for fast simulation of jump-diffusion processes and barrier options. J Deriv 10:43–54
Rogers L (1994) Fluid models in queueing theory and Wiener–Hopf factorization of Markov chains. Ann Appl Probab 4(2):390–413
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hieber, P. A Correction Note on: When the “Bull” Meets the “Bear”—A First Passage Time Problem for a Hidden Markov Process. Methodol Comput Appl Probab 16, 771–776 (2014). https://doi.org/10.1007/s11009-013-9355-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11009-013-9355-6