2010/05/09 by Shuqing Jiang, Jiang, Shuqing, Zongxia Liang +4
Economics, Econometrics and Finance · Mathematics · #60H05 (Secondary) #60H10 #91B24 (Primary) #91B28 #91B70 #Banking stability, regulation, efficiency #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #msc:60H05 #msc:60H10 #msc:91B24 #msc:91B28 #msc:91B70 #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1005.1357
30 pages, 7 figures
openalex publication_date 2010/05/09 · arxiv created 2010/09/16 · arxiv updated 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.