基于效用的永久性可转换债券定价  

Utility-Based Pricing of Perpetual Convertible Bonds

作　　者：王晓林[1] 杨招军[1] 

机构地区：[1]湖南大学金融与统计学院,长沙410079

出　　处：《管理科学》2013年第3期100-107,共8页Journal of Management Science

基　　金：国家自然科学基金(70971037;71171078;71221001);教育部博士点基金(20100161110022)~~

摘　　要：在不完备市场条件下,假设公司价值可以观测,公司只发行股票和不可赎回、不可违约的具有固定券息的永久性可转换债券,债券持有人有权利(但没有义务)按一定比例将债券转换为股票。基于可转换债券的结构式定价模型,给出债券持有人的最优转换策略,推导出可转换债券消费效用无差别价格的半封闭式解,利用有限差分方法,得到可转换债券的隐含价值(即消费效用无差别价格)以及可转换债券的最优消费策略和转换策略的数值解。研究结果表明,债券持有人的风险态度和非系统风险对最优转换策略和可转换债券的隐含价值有显著影响,与完备市场条件相比,风险厌恶情形可转换债券的转换触发水平和隐含价值较低,风险资产价格波动率越大,可转换债券的隐含价值越大。We assume that the value of a finn is observable in an incomplete market condition and the finn only issues shares and non-redeemable and non-defaulting perpetual convertible bonds with a fixed coupon rate. Bondholders have the right but not the obligation to convert the bonds into shares by a certain percentage. Based on the structural pricing model of convertible bonds, the study illustrates an optimal conversion strategy, deduces the semi-enclosed solution for the consumption utility-based indiffer- ence price of the bonds. Employing the finite difference method, we obtain the implied value （ consumption utility-based indiffer- ence price） and the numerical solution on optimal consumption strategy and converting strategy of convertible bonds. The results show that bondholders＇ risk attitude and non-systematic risk has a significant impact on the optimal converting strategy and the implied value of convertible bonds. In contrast to the complete market, conversion trigger level is lower and the implied value of convertible bonds is less in the risk aversion condition. In addition, the higher the volatility of risk asset price is, the more the implied value of convertible bonds is.

关 键 词：可转换债券 不完备市场 效用无差别定价 非系统风险 

分 类 号：F830.91[经济管理—金融学]