School of Mathematics and Applied Statistics


Stock loans have been recognized as a popular financial contract and considered as an alternative for investors to increase liquidity. Consequently, an accurate and efficient valuation of stock loans is necessary. Although there are some existing literatures on the valuation of stock loans, to the best of our knowledge, most are for perpetual loans. In reality, stock loan contracts mostly last for less than 10 years. It is, therefore, important to develop accurate and efficient evaluation methods for stock loans of finite maturity. This thesis explores a semi-analytic method for evaluating American puts in Zhu [2006] and proposes a modified semi-analytic method to evaluate stock loans in finite maturity. Three types of stock loans are formulated and solved as the corresponding American option problems under the Black-Scholes framework.

First, finite non-recourse stock loans with three different dividend distributions are formulated as American calls, and solved using Zhu’s semi-analytic method. Our results are compared with those in Dai and Xu [2011]. Then margin call stock loans are formulated as American Down-and-Out call options with rebate, and solved using the semi-analytic method. The dependency of the optimal exit price and the stock loan value on payback amount, and other parameters such as effective interest rate and volatility, are analyzed as well. Finally, Stock loans under a two-state regime switching economy are formulated as the corresponding Regime switching American Call options. A modified semi-analytic method is proposed to find the solutions of the optimal exit prices and stock loan values. Furthermore, fair service fee are calculated as well for different scenarios. The results of thesis could be used for borrowers and lenders to consider their exit policy and decide the service fee fairly.