Capped stock loans

In this paper we study a kind of financial product, stock loans, in which there is a capped limit for the stock price when it exceeds a predetermined barrier. Loans with two types of cap are analyzed: constant caps and caps with a constant growth rate. We build the pricing models of the contracts by analyzing the form of the optimal stopping time and derive the formulas of the value functions. We present the numerical results and make an analysis of fair values of related parameters. A comparison between capped stock loans and uncapped ones is also given. We find that capped loans have their own advantages such as more flexibility and lower cost.