A Dynamic Model for Hard-to-Borrow Stocks

24 Pages Posted: 12 Mar 2009

See all articles by Mike Lipkin

Mike Lipkin

Columbia University; Katama Trading, LLC

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences; Finance Concepts LLC

Date Written: March 10, 2009


We study the price-evolution of stocks that are subject to restrictions on short-selling, generically referred to as hard-to-borrow. Such stocks are either subject to regulatory short-selling restrictions or have insufficient float available for lending. Traders with short positions risk being bought-in, in the sense that their positions may be closed out by the clearing firm at market prices. The model we present consists of a coupled system of stochastic differential equations describing the stock price and the buy-in rate, an additional factor absent in standard models. The conclusion of the model is that short-sale restrictions result in increased prices and volatilities. Our model prices options as if the stock paid a continuous dividend, reflecting a modified form of Put-Call parity. Another consequence is that stocks that do not pay a dividend may have calls subject to early exercise. Both features are in agreement with empirical observations on hard-to-borrow stocks.

Keywords: stock-loan, hard-to-borrow stocks

Suggested Citation

Lipkin, Michael D. and Avellaneda, Marco, A Dynamic Model for Hard-to-Borrow Stocks (March 10, 2009). Available at SSRN: https://ssrn.com/abstract=1357069 or http://dx.doi.org/10.2139/ssrn.1357069

Michael D. Lipkin

Columbia University ( email )

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Katama Trading, LLC ( email )

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Marco Avellaneda (Contact Author)

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

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