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

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.

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References

  1. 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 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. 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 

  6. 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 

  7. Guo X (1999) Inside information and stock fluctuation. PhD thesis, Rutgers University, New Yersey

  8. 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 

  9. 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 

  10. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. Hieber P (2012) First-passage times of regime switching models. Working paper

  13. 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 

  14. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

  16. 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 

  17. 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 

  18. Kudryavtsev O (2010) Efficient pricing options under regime switching. Working paper

  19. 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 

  20. 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 

  21. 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 

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Correspondence to Peter Hieber.

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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

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Keywords

  • Markov switching
  • Regime switching
  • First-passage time
  • Laplace transform

AMS 2000 Subject Classifications

  • 60J27
  • 60G40
  • 44A10