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

While a classic result by Merton (1973, Bell J. Econ. Manage. Sci., 141-183) is that one should never exercise an American call option just before expiration if the underlying stock pays no dividends, the conclusion of a very recent empirical study conducted by Jensen and Pedersen (2016, J. Financ. Econ. 121(2), 278-299) suggests that one should 'never say never'. This paper complements Jensen and Pedersen's empirical study by presenting a theoretical study on how to price American call options under a hard-to-borrow stock model proposed by Avellaneda and Lipkin (2009, Risk 22(6), 92-97). Our study confirms that it is the lending fee that results in the early exercise of American call options and we shall also demonstrate to what extent lending fees have affected the early exercise decision.