Pricing finite maturity American style stock loans

Abstract

We use PDE approach to study American style stock loan with finite maturity. Pricing models of stock loans with dividend paid to the loaner as well as to the borrower are constructed. Stock loan value is calculated using normal and modified binomial tree method since there are no explicit solutions. Asymptotic solution of stock loans with dividend paid to the loaner was given in closed form. We also analyze the properties of optimal exercise boundaries of stock loans and find out the optimal exercise boundaries numerically. We further explored stock loans with underlying stock paying discrete dividend by modeling the jump condition on dividend payment date and applying similar analyses between two dividend payments.