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Pricing occupation-time options in a mixed-exponential jump-diffusion model

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  • Djilali Ait Aoudia
  • Jean-Franc{c}ois Renaud

Abstract

In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of intervals.

Suggested Citation

  • Djilali Ait Aoudia & Jean-Franc{c}ois Renaud, 2016. "Pricing occupation-time options in a mixed-exponential jump-diffusion model," Papers 1603.09329, arXiv.org.
    • Handle: RePEc:arx:papers:1603.09329
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    File URL: http://arxiv.org/pdf/1603.09329
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    References listed on IDEAS

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    1. Ning Cai & S. G. Kou, 2011. "Option Pricing Under a Mixed-Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 57(11), pages 2067-2081, November.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    4. Kwai Sun Leung & Yue Kuen Kwok, 2007. "Distribution of occupation times for constant elasticity of variance diffusion and the pricing of α-quantile options," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 87-94.
    5. Vadim Linetsky, 1999. "Step Options," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 55-96, January.
    6. Miura, Ryozo, 1992. "A Note on Look-Back Options Based on Order Statistics," Hitotsubashi Journal of commerce and management, Hitotsubashi University, vol. 27(1), pages 15-28, November.
    7. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double‐Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378, October.
    8. Ning Cai & Nan Chen & Xiangwei Wan, 2010. "Occupation Times of Jump-Diffusion Processes with Double Exponential Jumps and the Pricing of Options," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 412-437, May.
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    Cited by:

    1. Koo, Eunho & Kim, Geonwoo, 2017. "Explicit formula for the valuation of catastrophe put option with exponential jump and default risk," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 1-7.
    2. Walter Farkas & Ludovic Mathys & Nikola Vasiljevi'c, 2020. "Intra-Horizon Expected Shortfall and Risk Structure in Models with Jumps," Papers 2002.04675, arXiv.org, revised Jan 2021.

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