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

Journal Article


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. Through our numerical results, we find that the semi-explicit formula is a good approximate solution when the coupling parameter is small. However, when the stock price and the buy-in rate are significantly coupled, the PDE approach is preferred to solve the option pricing problem under the full hard-to-borrow model.

Publication Date


  • 2019

Citation


  • Ma, G., Zhu, S. & Chen, W. (2019). Pricing European call options under a hard-to-borrow stock model. Applied Mathematics and Computation, 357 243-257.

Scopus Eid


  • 2-s2.0-85064084515

Number Of Pages


  • 14

Start Page


  • 243

End Page


  • 257

Volume


  • 357

Place Of Publication


  • United States

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. Through our numerical results, we find that the semi-explicit formula is a good approximate solution when the coupling parameter is small. However, when the stock price and the buy-in rate are significantly coupled, the PDE approach is preferred to solve the option pricing problem under the full hard-to-borrow model.

Publication Date


  • 2019

Citation


  • Ma, G., Zhu, S. & Chen, W. (2019). Pricing European call options under a hard-to-borrow stock model. Applied Mathematics and Computation, 357 243-257.

Scopus Eid


  • 2-s2.0-85064084515

Number Of Pages


  • 14

Start Page


  • 243

End Page


  • 257

Volume


  • 357

Place Of Publication


  • United States