Option Problems On Stock Loan

This paper introduces two new kinds of stock loans and establishes the fair valueprocesses for two di?erent stock loans via variational method and probabilistic ap-proach. It also works out procedures for determining fair values of parameters asso-ciated with these stock loans. Moreover, it gives a general setting to deal with stockloans. The stock loan is treated as a generalized perpetual American call option withautomatic termination clause , cap and possibly negative interest rate. Since the twonew kinds of stock loans helps the bank control the risk, the bank should charge lessservice fee compared to the usual stock loans and can get the balance between risk andreturn. We treat the problems as a di?usion on an interval via variational and proba-bilistic approach.