北京航空航天大学学报(社会科学版) ›› 2019, Vol. 32 ›› Issue (4): 78-86.DOI: 10.13766/j.bhsk.1008-2204.2017.0133

• 经济与管理 • 上一篇    下一篇

分数布朗运动下或有可转债定价模型

尤左伟, 刘善存   

  1. 北京航空航天大学 经济管理学院, 北京 100083
  • 收稿日期:2017-05-09 出版日期:2019-07-25 发布日期:2019-09-06
  • 作者简介:尤左伟(1984-),男,浙江温州人,博士研究生,研究方向为衍生品定价、动态资产定价理论.
  • 基金资助:

    国家自然科学基金面上项目(71371023)

Pricing CoCos in Fractional Brownian Motion Environment

YOU Zuowei, LIU Shancun   

  1. School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2017-05-09 Online:2019-07-25 Published:2019-09-06

摘要:

或有可转债是重要的自救债务工具。实证结果表明,在上交所交易的银行股票收益率序列普遍存在较弱的长程自相关性。假设标的银行的股票价格动态方程由分数布朗运动驱动,其中分数布朗运动的Hurst指数H满足1/2 < H < 1,用于刻画股价的长记忆性、分形性。再应用基于偏好的均衡定价方法与分数布朗运动的条件分布对或有可转债定价。基于障碍期权与远期合约的定价公式,推导得或有可转债的显式定价公式。结果表明,虽然标的股票收益率序列的长程自相关性较弱,但由于或有可转债期限较长,其对或有可转债股权关联部分的价值有着显著的影响。标的股票收益率序列的长程自相关性对障碍期权的影响不可忽略。

关键词: 银行股价, 或有可转债, 障碍期权, 分数布朗运动, 长程自相关, 均衡定价方法

Abstract:

Contingent Convertible Bonds (CoCos) are an important type of bail-in debts. The empirical results show that the price changes of the banks' stocks in the Shanghai Stock Exchange do exhibit a long-range serial autocorrelation and persistence in following a trend. The stock price of the underlying bank is described by a stochastic differential equation driven by a fractional Brownian motion with the Hurst parameter H satisfying 1/2 < H < 1, which characterizes the serial autocorrelation indicating a memory and the fractal character of the price. The preference based equilibrium approach and the conditional distribution of the fractional Brownian motion are employed to price the CoCos. The explicit pricing formula for CoCos is derived through pricing barrier options and forwards. The results indicate that the long-range serial autocorrelation in price changes of the underlying stock has a significant influence on the values of the equity-related components of the CoCos since the maturity is usually large, though the autocorrelation is weak. The values of the barrier options are significantly affected by the long-range autocorrelation of the returns on the underlying stocks.

Key words: banks' share prices, contingent convertible bonds, barrier options, fractional brownian motion, long-range autocorrelation, preference based equilibrium approach

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