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Option Pricing and Filtering with Hidden Markov-Modulated Pure-Jump Processes

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  • Robert J. Elliott
  • Tak Kuen Siu

Abstract

This article discusses the pricing of derivatives in a continuous-time, hidden Markov-modulated, pure-jump asset price model. The hidden Markov chain modulating the pure-jump asset price model describes the evolution of the hidden state of an economy over time. The market model is incomplete. We employ a version of the Esscher transform to select a price kernel for valuation. We derive a valuation formula for European options using a Fourier transform and the correlation theorem. This formula depends on the hidden Markov chain. It is then estimated using a robust filter of the chain.

Suggested Citation

  • Robert J. Elliott & Tak Kuen Siu, 2013. "Option Pricing and Filtering with Hidden Markov-Modulated Pure-Jump Processes," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(1), pages 1-25, March.
  • Handle: RePEc:taf:apmtfi:v:20:y:2013:i:1:p:1-25
    DOI: 10.1080/1350486X.2012.655929
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    Citations

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    Cited by:

    1. Gradojevic Nikola, 2016. "Multi-criteria classification for pricing European options," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(2), pages 123-139, April.
    2. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Pricing annuity guarantees under a double regime-switching model," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 62-78.
    3. repec:spr:annopr:v:262:y:2018:i:2:d:10.1007_s10479-016-2210-8 is not listed on IDEAS
    4. Jun Yu, 2014. "Optimal Asset-Liability Management for an Insurer Under Markov Regime Switching Jump-Diffusion Market," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 317-330, November.
    5. Mauricio Junca & Rafael Serrano, 2014. "Utility maximization in pure-jump models driven by marked point processes and nonlinear wealth dynamics," Papers 1411.1103, arXiv.org, revised Sep 2015.
    6. Robert Elliott & Tak Siu, 2015. "Asset Pricing Using Trading Volumes in a Hidden Regime-Switching Environment," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 133-149, May.
    7. Oscar Lopez & Rafael Serrano, 2014. "Martingale approach to optimal portfolio-consumption problems in Markov-modulated pure-jump models," Papers 1406.3112, arXiv.org.
    8. Donatien Hainaut & Yan Shen & Yan Zeng, 2016. "How do capital structure and economic regime affect fair prices of bank's equity and liabilities?," Post-Print hal-01394133, HAL.
    9. Lin, Shih-Kuei & Peng, Jin-Lung & Chao, Wei-Hsiung & Wu, An-Chi, 2016. "The extension from independence to dependence between jump frequency and jump size in Markov-modulated jump diffusion models," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 217-235.
    10. Siu, Tak Kuen, 2016. "A self-exciting threshold jump–diffusion model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 168-193.
    11. Shen, Yang & Siu, Tak Kuen, 2013. "Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 757-768.

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