| 分数布朗运动下带违约风险的可转换债券定价 |
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| 引用本文： | 刘善存,宋殿宇,金华.分数布朗运动下带违约风险的可转换债券定价[J].中国管理科学,2011,19(6):25-30. |
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| 作者姓名： | 刘善存 宋殿宇 金华 |
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| 作者单位： | 1. 北京航空航天大学经济管理学院, 北京 100191;2. 北京外国语大学国际商学院, 北京 100089 |
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| 基金项目： | 国家自然科学基金重点项目(70831001),国家自然科学基金面上项目(71071010) |
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| 摘 要： | 应用均衡定价方法,考虑股票价格和公司资产价值服从分数布朗运动以及存在公司违约风险情况下的可转债定价问题;建立相应的可转债定价模型,采用拟鞅定价方法,得出了欧式看涨期权的显式解,进而得出了可转债定价公式;最后利用数值算例进行分析,结论表明公司违约风险、股票价格和公司资产价格的长程关联性是可转债定价时不可忽略的因素。
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| 关 键 词： | 可转换债券 分数布朗运动 长程关联性 看涨期权 拟鞅 |
| 收稿时间： | 2010-12-20 |
| 修稿时间： | 2011-8-24 |
Pricing Convertible Bonds with Default Risk in the Fractional Brownian Environment |
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| LIU Shan-cun,SONG Dian-yu,JIN Hua.Pricing Convertible Bonds with Default Risk in the Fractional Brownian Environment[J].Chinese Journal of Management Science,2011,19(6):25-30. |
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| Authors: | LIU Shan-cun SONG Dian-yu JIN Hua |
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| Affiliation: | 1. School of Economics and Management, Beihang University, Beijing 100191, China;2. International Business school, Beijing Foreign Studies University, Beijing 100089, China |
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| Abstract: | By applying equilibrium approach,this paper studies the pricing of convertible bonds with default risk when underlying assets follow the fractional Brownian motion.A mathematical pricing model for convertible bonds has been developed and an analytical solution has been proved by quasi-martingale method.An analysis on a numerical example is presented in the end of this paper.The conclusion is that the default risk and the long-range dependence of underlying asset are key factors for pricing convertible bonds... |
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| Keywords: | convertible bonds fractional Brownian motion long-range dependence call option quasi-martingale |
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