随机参数股价波动源模型下可赎回可转债定价  

The martingale pricing method for pricing fluctuation concerning stock models of callable bonds with random parameters

作　　者：郑晓阳[1] 官畅[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2011年第1期124-128,共5页Journal of Harbin Engineering University

基　　金：哈尔滨工程大学基础研究基金资助项目(HEUF04022)

摘　　要：为了深入研究同时具有债权性质和期权性质的可转换债券的定价问题,也作为对鞅方法在期权定价过程中应用的进一步推广,考虑到金融危机背景,选取了由随机波动源和异常波动源2种波动同时作用并且能够更好刻画市场中股票价格实际波动现象的股价波动源模型,在无风险利率、股价期望收益率以及波动率均为依赖时间的随机参数的条件下,利用随机微分方程、测度变换以及鞅理论相关知识,讨论了附有赎回条款的可转换债券定价问题,得到了上述前提下可赎回可转债的初始价格定价公式.本文对现有研究成果进行了改进,从而更贴近实际情况.文中结果为进一步研究可转换债券定价问题奠定了基础,推广了鞅理论的应用.In order to study the pricing of convertible bonds with both bond and option properties,and also for further application of the martingale method to option pricing,a model of stock pricing fluctuation,which has random and abnormal fluctuations and can better describe the actual market situation,was adopted.This was done considering the background of the financial crisis and with the assumption that the risk free rate,the expected return rate,and the volatility are random time function parameters.Furthermore,knowledge about stochastic differential theory,measure transformation,and the martingale theory was applied to analyze the pricing of callable bonds.Finally,the pricing formula for the initial price was obtained.The existing achievements were further improved to a more practical level.The result has laid a foundation for further research about convertible pricing bonds,and extended the application of the martingale theory.

关 键 词：股价波动源模型 可赎回债券 随机参数 鞅方法 

分 类 号：F830.9[经济管理—金融学]