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On the optimal exercise boundaries of swing put options

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  • Tiziano De Angelis
  • Yerkin Kitapbayev

Abstract

We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of "put" type and the underlying dynamics follows a geometric Brownian motion. The optimal stopping region relative to each optimal stopping time is described in terms of two boundaries which are continuous, monotonic functions of time and uniquely solve a system of coupled integral equations of Volterra-type. Finally we provide a formula for the value function of the problem.

Suggested Citation

  • Tiziano De Angelis & Yerkin Kitapbayev, 2014. "On the optimal exercise boundaries of swing put options," Papers 1407.6860, arXiv.org, revised Jan 2017.
    • Handle: RePEc:arx:papers:1407.6860
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    References listed on IDEAS

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    1. Imene Ben Latifa & Joseph Frederic Bonnans & Mohamed Mnif, 2011. "Optimal multiple stopping problem and financial applications," Working Papers hal-00642919, HAL.
    2. Ben Hambly & Sam Howison & Tino Kluge, 2009. "Modelling spikes and pricing swing options in electricity markets," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 937-949.
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    5. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128, January.
    6. N. Meinshausen & B. M. Hambly, 2004. "Monte Carlo Methods For The Valuation Of Multiple‐Exercise Options," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 557-583, October.
    7. Christian Bender, 2011. "Dual pricing of multi-exercise options under volume constraints," Finance and Stochastics, Springer, vol. 15(1), pages 1-26, January.
    8. Christophe Barrera-Esteve & Florent Bergeret & Charles Dossal & Emmanuel Gobet & Asma Meziou & Rémi Munos & Damien Reboul-Salze, 2006. "Numerical Methods for the Pricing of Swing Options: A Stochastic Control Approach," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 517-540, December.
    9. M. Wahab & Chi-Guhn Lee, 2011. "Pricing swing options with regime switching," Annals of Operations Research, Springer, vol. 185(1), pages 139-160, May.
    10. Olivier Bardou & Sandrine Bouthemy & Gilles Pages, 2009. "Optimal Quantization for the Pricing of Swing Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(2), pages 183-217.
    11. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
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    Cited by:

    1. Katia Colaneri & Tiziano De Angelis, 2019. "A class of recursive optimal stopping problems with applications to stock trading," Papers 1905.02650, arXiv.org, revised Jun 2021.
    2. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2020. "Optimal hedging of a perpetual American put with a single trade," Papers 2003.06249, arXiv.org, revised Sep 2020.
    3. Thomas Kruse & Philipp Strack, 2019. "An Inverse Optimal Stopping Problem for Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 423-439, May.

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