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Change of measure under the hard-to-borrow model

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  • Peng Liu

Abstract

As the Securities and Exchange Commission(SEC) has implemented a new regulation on short-sellings, short-sellers are required to repurchase stocks once the clearing risk rises to a certain level. Avellaneda and Lipkin proposed a fully coupled SDE system to describe the mechanism which is referred as Hard-To-Borrow(HTB) models. Guiyuan Ma obtained the PDE system for both American and European options. There is a technical error in Guiyuan Ma where two correlated Brownian motion should be converted before change of measure. In this paper, I will provide supplement conditions.

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  • Peng Liu, 2020. "Change of measure under the hard-to-borrow model," Papers 2001.10384, arXiv.org.
    • Handle: RePEc:arx:papers:2001.10384
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    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. 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.
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