A stock loan is a financial contract that allows the borrower to obtain a loan
with stocks as collaterals. In this talk, we will discuss the “American”
connection between stock loans and options. The stock loan partial differential
equations (PDEs) are established under the Black-Scholes framework.
Mathematically, the valuation problem of stock loans is a moving boundary
problem, which does not have analytical solution except for special cases. We
show that the problem can be solved semi-analytically with great accuracy and
efficiency. Numerical examples are presented to demonstrate our solution