Valuation of finite maturity stock loans under regime switching and mean reverting stock models

Abstract

Stock loans are business contracts between borrowers and lenders in which the borrower uses shares of stock as collateral for the loan. Since the value of the collateral is subject to wide and frequent price fluctuations, valuing such a transaction behaves more like an option pricing problem than a debt valuation problem. This dissertation will list, prove, and analyze formulas for stock loan valuation with finite horizon when the collateral stock obeys a classical geometric Brownian motion, a mean reverting, or a two-state regime switching with both mean reverting and geometric Brownian motion states. Also, existence and uniqueness of viscosity solutions will be proved for the mean reverting and classical geometric Brownian motion regime switching with partial information stock models. Numerical examples are reported to illustrate the results.