Skip to main content
Log in

A Correction Note on: When the “Bull” Meets the “Bear”—A First Passage Time Problem for a Hidden Markov Process

  • Published:
Methodology and Computing in Applied Probability Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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

    Article  MATH  MathSciNet  Google Scholar 

  • Barlow M, Rogers L, Williams D (1990) Wiener–Hopf factorization for matrices. Lect Notes Math 784:324–331

    Article  MathSciNet  Google Scholar 

  • Boyle P, Draviam T (2007) Pricing exotic options under regime switching. Insur Math Econ 40:267–282

    Article  MATH  MathSciNet  Google Scholar 

  • Buffington J, Elliott RJ (2002) American options with regime switching. Int J Theor Appl Financ 5:497–514

    Article  MATH  MathSciNet  Google Scholar 

  • Elliott RJ, Chan L, Siu TK (2005) Option pricing and Esscher transform under regime switching. Ann Finance 1(4):423–432

    Article  MATH  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • Guo X (2001b) An explicit solution to an optimal stopping problem with regime switching. J Appl Probab 38:464–481

    Article  MATH  MathSciNet  Google Scholar 

  • Guo X (2004) Closed-form solutions for perpetual American put options with regime switching. SIAM J Appl Math 64(6):2034–2049

    Article  MATH  MathSciNet  Google Scholar 

  • Henriksen PN (2011) Pricing barrier options by a regime switching model. J Quant Financ 11(8):1221–1231

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • Jobert A, Rogers, L (2006) Option pricing with Markov modulated dynamics. SIAM J Control Optim 44:2063–2078

    Article  MATH  MathSciNet  Google Scholar 

  • Khaliq A (2010) New numerical scheme for pricing American option with regime-switching. J Theor Appl Financ 12(3):319–340

    Article  MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • Metwally S, Atiya A (2002) Using Brownian bridge for fast simulation of jump-diffusion processes and barrier options. J Deriv 10:43–54

    Article  Google Scholar 

  • Rogers L (1994) Fluid models in queueing theory and Wiener–Hopf factorization of Markov chains. Ann Appl Probab 4(2):390–413

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Peter Hieber.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11009-013-9355-6

Keywords

AMS 2000 Subject Classifications

Navigation