Stock loan with automatic termination clause, cap and margin

Abstract

This paper works out fair values of the stock loan model with automatic termination clause, cap and margin. This stock loan is treated as a generalized perpetual American option with possibly negative interest rate and some constraints. Since it helps a bank to control the risk, the banks charge lower service fees compared to stock loans without any constraints. The automatic termination clause, cap and margin are in fact a stop order set by the bank. Mathematically, it is a kind of optimal stopping problem arising from the pricing of financial products which is first revealed. We aim at establishing explicitly the value of such a loan and ranges of fair values of key parameters : this loan size, interest rate, cap, margin and fee for providing such a service and quantity of this automatic termination clause and the relationships among these parameters as well as the optimal exercise times. We present numerical results and make analysis about the model parameters and how they impact on value of stock loan.