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

Guiyuan Ma, Song-Ping Zhu and Wenting Chen

Applied Mathematics and Computation, 2019, vol. 357, issue C, 243-257

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.

Keywords: Hard-to-borrow stock; Buy-in rate; Regulation SHO; Option pricing; ADI scheme (search for similar items in EconPapers)
Date: 2019
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Handle: RePEc:eee:apmaco:v:357:y:2019:i:c:p:243-257