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A stock loan is a contract between two parties: the lender, usually a bank or other financial institution providing a loan, and the borrower, represented by a client who owns one share of a stock used as collateral for the loan. Several reasons might motivate the client to get into such a deal. For example he might not want to sell his stock or even face selling restrictions, while at the same time being in need of available funds to attend to another financial operation. In Xia and Zhou (2007), a stock loan is modeled as a perpetual American option with a time varying strike and analyzed in detail within the Black-Scholes framework. In this paper, we extend the valuation of such loans to an incomplete market setting, which takes into account the natural trading restrictions faced by the client. When the maturity of the loan is infinite we obtain an exact formula for the value of the loan fee to be charged by the bank based on a result in Henderson (2007). For loans of finite maturity, we characterize its value using a variational inequality first presented in Oberman and Zariphopoulou (2003). In both cases we show analytically how the fee varies with the model parameters and illustrate the results numerically. This is joint work with Cesar G. Velez (Universidad Nacional de Colombia).