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Pricing European call options under a hard-to-borrow stock model

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  • Ma, Guiyuan
  • Zhu, Song-Ping
  • Chen, Wenting

Abstract

This paper studies European call option pricing problem under a hard-to-borrow stock model where stock price and buy-in rate are fully coupled. Avellaneda and Lipkin (2009) proposed a simplified solution approach with an independence assumption, and then derived a semi-explicit pricing formula. However, such an approach has limited its application to more general cases. In this paper, we propose a partial differential equation (PDE) approach for pricing European call options, regardless of the independence assumption. A two-dimensional PDE is derived first with a set of appropriate boundary conditions. Then, two numerical schemes are provided with different treatments of the jump term.

Suggested Citation

  • Ma, Guiyuan & Zhu, Song-Ping & Chen, Wenting, 2019. "Pricing European call options under a hard-to-borrow stock model," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 243-257.
    • Handle: RePEc:eee:apmaco:v:357:y:2019:i:c:p:243-257
    DOI: 10.1016/j.amc.2019.04.002
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    References listed on IDEAS

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    1. Jensen, Mads Vestergaard & Pedersen, Lasse Heje, 2016. "Early option exercise: Never say never," Journal of Financial Economics, Elsevier, vol. 121(2), pages 278-299.
    2. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Ekkehart Boehmer & Charles M. Jones & Xiaoyan Zhang, 2013. "Shackling Short Sellers: The 2008 Shorting Ban," The Review of Financial Studies, Society for Financial Studies, vol. 26(6), pages 1363-1400.
    5. Richard B. Evans & Christopher C. Geczy & Adam V. Reed, 2009. "Failure Is an Option: Impediments to Short Selling and Options Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1955-1980, May.
    6. Duffie, Darrell & Garleanu, Nicolae & Pedersen, Lasse Heje, 2002. "Securities lending, shorting, and pricing," Journal of Financial Economics, Elsevier, vol. 66(2-3), pages 307-339.
    7. Jones, Charles M. & Lamont, Owen A., 2002. "Short-sale constraints and stock returns," Journal of Financial Economics, Elsevier, vol. 66(2-3), pages 207-239.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Nigel Clarke & Kevin Parrott, 1999. "Multigrid for American option pricing with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 177-195.
    10. Diamond, Douglas W. & Verrecchia, Robert E., 1987. "Constraints on short-selling and asset price adjustment to private information," Journal of Financial Economics, Elsevier, vol. 18(2), pages 277-311, June.
    11. Lars Tyge Nielsen, 1989. "Asset Market Equilibrium with Short-Selling," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(3), pages 467-473.
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    Cited by:

    1. Peng Liu, 2020. "Change of measure under the hard-to-borrow model," Papers 2001.10384, arXiv.org.

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