质押贷款质押率决定的期权定价方法

中国管理科学 ›› 2013, Vol. ›› Issue (1): 16-22.

质押贷款质押率决定的期权定价方法

张燃¹, 徐爽², 王凤敏³

1. 北京科技大学东凌经济管理学院, 北京 100083;
2. 四川省宜宾市商业银行, 四川宜宾 644000;
3. 北京工业大学数理学院, 北京 100871

收稿日期:2011-09-10 修回日期:2012-10-04 出版日期:2013-02-28 发布日期:2013-02-26
基金资助:
国家自然科学基金资助项目(71003005)

Pledged Loan-to-value Ratio Determination Based on Option Pricing Method

ZHANG Ran¹, XU Shuang², WANG Feng-min³

1. Dongling School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China;
2. Yibin City Commercial Bank, Yibin 644000, China;
3. School of Applied Mathematics, Beijing University of Technology, Beijing 100124, China

Received:2011-09-10 Revised:2012-10-04 Online:2013-02-28 Published:2013-02-26

摘要/Abstract

摘要： 本文使用期权定价方法研究库存质押贷款质押率的确定问题。质押贷款超额收益现值可看作一个看跌期权的价值。在此框架内,首先分析固定利率零息贷款的质押率和贷款期限、超额收益率以及质物价值波动特征的相互关系。同样的分析被扩展到付息贷款和组合质物等情形,并针对固定利率零息贷款情形给出了数值算例。数值模拟结果给出了质押率的期限结构:贷款期限不同,质押率不同;质押率是贷款期限的凸性减函数。研究结果还表明:质押率是质物价值波动率的凹性减函数,质物价值波动越大,质押率越低,这可用来分析不同金属做质押物时质押率的变化;质押率是风险溢价的凹性增函数,风险溢价越大,银行的风险承受能力越强,质押率越高。

关键词: 质押贷款, 质押率, 看跌期权, 质押率的期限结构, 质物价值波动

Abstract: In this paper, the determination of pledged loan-to-value ratio under an option pricing environment is investigated. The basic idea is that the present value of pledged loan payoff is equal to a put option’s value. While the interest rate is fixed and the loan is without coupon, the interrelation of pledged ratio and some factors, such as maturity, excess return and the value volatility of pledge are analyzed. Then, the same work is extended to coupon loan and portfolio pledge circumstances. For zero coupon and fixed interest rate circumstances, a numerical example is performed. The findings are as follows: firstly, the numerical result indicate that loan-to-value ratio is a convex decreasing function of maturity. Secondly, loan-to-value ratio is a concave decreasing function of value volatility of pledge. Thirdly, loan-to-value ratio is a concave increasing function of risk premium. For floating interest rate circumstances, the function form between loan interest and risk free rate shouldbe specified.

Key words: pledged loan, loan-to-value ratio, put option, term structure of pledged ratio, value volatility of pledge

中图分类号:

F830.9

张燃, 徐爽, 王凤敏. 质押贷款质押率决定的期权定价方法[J]. 中国管理科学, 2013, (1): 16-22.

ZHANG Ran, XU Shuang, WANG Feng-min. Pledged Loan-to-value Ratio Determination Based on Option Pricing Method[J]. Chinese Journal of Management Science, 2013, (1): 16-22.

参考文献

[1] Stulz R,Johnson H. An analysis of secured debt[J].Journal of Financial Economics,1985,14(4):501-521.
[2] Merton R C. Theory of rational option pricing[J]. Journal of Economics and Management Science, 1973, 4(1): 141-183.
[3] Jokivuolle E, Peura S. Incorporating collateral value uncertainty in loss given default estimates and loan-to-value ratios[J]. European Financial Management, 2003, 9(3): 299-314.
[4] Cossin D,Hricko T. A structural analysis of credit risk with risky collateral:a methodology for haircut determination [J]. Ecomomic Notes, 2003, (2): 243-282.
[5] Cossin D, Huang Zhijiang, Aunon-Nerin D. A framework for collateral risk control determination[R].Working Paper, European central bank, 2003.
[6] Jarrow R A, Turnbull S. Pricing derivatives on financial securities subject to credit risk[J]. Journal of Finance, 1995, 50(1):53-85.
[7] Jarrow R A, Lando D, Turnbull S.Markov model for the term structure of credit risk spreads[J]. Review of Financial Studies, 1997, 10(2): 481-523.
[8] Duffie D,Singleton K. Modeling term structure of defaultable bonds[J]. Review of Financial Studies,1999,12:687-720.
[9] Buzacott J A, Zhang R Q.Inventory management with asset-based financing[J]. Management Science, 2004,24: 1274-1292.
[10] 王志诚.股票质押贷款质押率评定的VaR方法[J].金融研究,2003,(12):64-71.
[11] 范英,魏一鸣.基于稽查VaR的股票组合质押率评估方法[J].系统工程,2003,(4):86-89.
[12] 黄中文,刘亚娟,朱芳芳.股票质押贷款业务及质押率探析[J].金融理论与实践,2009,(9):92-95.
[13] 李毅学,冯耕中,徐渝.价格随机波动下存货质押融资业务质押率研究[J].系统工程理论与实践,2007,(12):42-48.
[14] 齐二石,马姗姗,韩铁.组合仓单质押贷款质押率研究[J].西安电子科技大学学报(社会科学版),2008,(11):50-53.
[15] 张钦红,赵泉午.需求随机时的存货质押贷款只要率决策研究[J].中国管理科学, 2010, (5):21-27.
[16] Postali F A S, Picchetti P. Geometric brownian motion and structural breaks in oil prices: a quantitative analysis[J]. Energy Economics, 2006,28(4): 506-522.
[17] Alvarez-Ramirez J, Alvarez J, Rodriguez E, Short-term predictability of crude oil markets: a detrended fluctuation analysis approach[J]. Energy Economics, 2008,30(5): 2645-2656.
[18] Milevsky M A, Posner S E. A closed-form approximation for valuing basket options[J]. The Journal of Derivatives,1998,5(4):54-61.