Stock loan with Automatic termination clause, cap and margin

TL;DR

This paper derives fair value formulas for stock loans with automatic termination, cap, and margin, modeling them as generalized perpetual American options with constraints, and analyzes how parameters influence their valuation.

Contribution

It introduces a novel valuation model for constrained stock loans with automatic termination, providing explicit formulas and parameter analysis.

Findings

Explicit fair value formulas for the stock loan with constraints.

Parameter ranges and their impact on loan value.

Numerical analysis illustrating model behavior.

Abstract

This paper works out fair values of 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 less 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 problems 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 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.