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On perpetual American put valuation and first-passage in a regime-switching model with jumps

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Abstract

In this paper we consider the problem of pricing a perpetual American put option in an exponential regime-switching Lévy model. For the case of the (dense) class of phase-type jumps and finitely many regimes we derive an explicit expression for the value function. The solution of the corresponding first-passage problem under a state-dependent level rests on a path transformation and a new matrix Wiener–Hopf factorization result for this class of processes.

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Author notes

  1. Zhengjun Jiang

    Present address: School of Finance, Nanjing University of Finance and Economics, Nanjing, 210046, China

Authors and Affiliations

  1. Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, UK

    Zhengjun Jiang & Martijn R. Pistorius

Authors
  1. Zhengjun Jiang
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  2. Martijn R. Pistorius
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Corresponding author

Correspondence to Martijn R. Pistorius.

Additional information

In memory of Yumin Jiang.

Research supported by the Nuffield Foundation, grant NAL/00761/G, and EPSRC grant EP/D039053/1.

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Jiang, Z., Pistorius, M.R. On perpetual American put valuation and first-passage in a regime-switching model with jumps. Finance Stoch 12, 331–355 (2008). https://doi.org/10.1007/s00780-008-0065-9

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  • DOI: https://doi.org/10.1007/s00780-008-0065-9

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