混合分数布朗运动下可转债定价模型研究  

Convertible bond pricing in a mixed fractional Brownian motion environment

作　　者：尤左伟[1] 刘善存[1] 张强[2] YOU Zuowei LIU Shancun ZHANG Qiang(School of Economics and Management, Beihang University, Beijing 100191, China School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China)

机构地区：[1]北京航空航天大学经济管理学院 [2]北京化工大学经济管理学院

出　　处：《系统工程理论与实践》2017年第4期843-854,共12页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71371023;71371024;71171146)~~

摘　　要：标的股价用混合分数布朗运动驱动的随机微分方程刻画,其中分数布朗运动的Hurst参数H满足1/2<H<1,用于描述股价的长记忆性,利率服从Vasicek过程,违约风险用约化方法处理,建立可转债定价模型.通过引入投资者的风险偏好态度以及对效用函数的限制使得可转债的风险中性定价关系存在,基于市场均衡条件得到平均风险中性测度,利用风险中性定价原理得出可转债定价公式,及其关于Hurst参数的导数的显式表达式.结果表明Hurst参数通过影响条件股价过程的积分波动率而影响可转债价值.We establish a convertible bond （CB） pricing model. The underlying stock price is described by a stochastic differential equation driven by a mixed fractional Brownian motion with the Hurst parameter H satisfying 1/2 〈 H 〈 1, which characterizes the serial autocorrelation implicating sort of a memory of the stock price. The interest rate follows the Vasicek process. The default risk is addressed by the reducedform approach. The existence of the risk neutral valuation relationship （RNVR） of the convertible bond is obtained by the employment of risk preference attitude of the investors and restrictions on investors＇ utility function. An explicit pricing formula for the convertible bond with default risk is derived. As a result, the derivative of the convertible bond price with respect to the Hurst parameter H is also shown explicitly, The results show that the influence of the Hurst parameter on the CB price is based on its influence on the integrated volatility of the conditional underlying stock price.

关 键 词：混合分数布朗运动 可转债 风险中性定价原理 VASICEK利率模型 条件分布 

分 类 号：F830[经济管理—金融学]