Pricing Strategies Of Stock Loans

In this paper, we study the pricing strategies of stock loans under different circumstances. Besides, by numerical study and sensitive analysis, we got some useful conclusions.In the first section, introduction, literature review and paper structure are presented.In the second section, we study the stock loan pricing problem under geometric Brown motion. First, we introduced Xia and Zhou’s work, in which they treat the stock loan as a generalized American call option. By analysis, they found the relationship between loan amount, interest and service cost. Secondly, based on Xia and Zhou’s work, we modified the model by setting constant and changing upper constraint and presented the solution methods. Thirdly, from the numerical examples, we found that by setting a upper bound, borrower can bear a lower cost and can have more liquidity.In the third section, we studied the pricing problem of stock loan under jump-diffusion. Firstly, we introduced the fundamental theory of jump-diffusion and established a basic model of jump-diffusion process. Secondly, by using optimal stopping time and bankrupt theories, we build the pricing model of the loan stock problem and presented the associated pricing formulation. Lastly, by numerical analysis, some conclusions are drawn. For example, in the model, the loan cost is concave in λ. For constant λ, loan cost is increasing in loan amountq. When loan amountq is fixed, loan cost is decreasing in η. And for constant η, loan cost is increasing in q.In the last section, we conclude the findings in section 2 and section 3. Besides, we presented the limitations and future research of this paper.