杠杆交易限制下可转债的交换期权定价模型  

Exchange option pricing model of convertible bonds under leveraged transactions constraints

作　　者：程志富[1] 胡昌生[1] CHENG Zhifu;HU Changsheng(Economics and Management School of Wuhan University,Wuhan 430072,China)

机构地区：[1]武汉大学经济与管理学院,湖北武汉430072

出　　处：《管理工程学报》2020年第1期195-199,共5页Journal of Industrial Engineering and Engineering Management

基　　金：国家自然科学基金资助项目(71671134);国家自然科学基金资助青年项目(71401128)。

摘　　要：不同于标准期权,可转债转股条款的实质是一份交换期权。考虑了市场中的杠杆交易限制,利用远期风险中性测度原理和超复制方法,重新构建了一个可转债交换期权模型。结合2015年2月至2015年10月的可转债市场数据,通过比较基于套利限制的交换期权定价方法与基于无套利原理的标准期权定价方法的计算结果,发现前者能够为可转债的真实价值确定一个参考区间,而后者仅仅是前者的一个特例,且后者大致相当于价值参考区间的下界。通过调整杠杆交易限制的参数,发现:一方面,随着市场杠杆交易限制的增加,转股权(从而转债)的价值会由于其复制成本的上升而增加;另一方面,当转股权处于深度虚值或深度实值状态时,转股权(从而转债)的理论价值区间会缩小。这就为杠杆交易限制与转债价格无套利区间之间所存在的正向关系,以及转股权实/虚值程度与转债价格无套利区间之间所存在的反向关系提供了理论上的依据。Convertible bond has been one of the innovative financial instruments in the investment and financing markets in recent decades.To study the law of value of convertible bonds,it is necessary to consider the objective characteristics of market development,but also grasp the essence of convertible bonds.Leverage trading is a new thing for the A-share market.Since July 2014,its scale has soared,intensified the fluctuation of the market and led to the boom and slump of the recent market.It has made leveraged transactions constraints a priority for capital market regulation.At present,there are some incomplete cases in the actual market economy in China.Among those,leveraged transactions constraints are a typical reality in the current underlying market.Besides,some literature combines theory and practice in real life to compare the converting option of the convertible bond and the common stock option and find the former is an exchange option which is equivalent of a right to exchange stock with a bond,while the latter is a vanilla option in substance.The convertible exchange option model is rebuilt based on the margin trading in the A-share market as well as the particularity of the conversion option,The traditional approach to model convertible bond is Tsiveriotis and Fernande(1998)with a finite difference method or the pricing theory of Black and Scholes(1973)model.This approach separates the value of convertible bond into two parts:cash part and equity part,and it is made with no-arbitrage theory.Since many assumptions of classical models do not reflect actual situations in the real world,we modify the value model according to leveraged transactions constraints in the present to modify option pricing function on the arbitrage-free condition.In this paper,using the forward risk-neutral measure and super-replication method,the exchange option pricing model of convertible bonds is built under leveraged transactions constraints.This paper empirically validates the exchange option pricing model by comparing Tsiveriotis

关 键 词：可转债定价 交换期权 杠杆交易限制 超复制 

分 类 号：F830.91[经济管理—金融学]