| 不完备市场下一类衍生证券的无风险定价与保值 |
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| 引用本文： | 秦国文,杨招军.不完备市场下一类衍生证券的无风险定价与保值[J].系统工程,2007,25(9):22-25. |
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| 作者姓名： | 秦国文 杨招军 |
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| 作者单位： | 1. 湖南省社会科学院,湖南,长沙,410003;湖南大学,经济与贸易学院,湖南,长沙,410079
2. 湖南大学,数学院,湖南,长沙,410082;湖南大学,经济与贸易学院,湖南,长沙,410079 |
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| 基金项目： | 国家社会科学基金;湖南省自然科学基金;湖南省社会科学基金 |
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| 摘 要： | 对于不完备市场模型，衍生证券定价及保值一般与投资者风险态度有关。本文研究的不完备市场模型是B-S模型的推广，它同时也说明了这样一个事实：即使是在不完备市场条件下，我们也能找到相当多的衍生证券，它们具有与投资者风险态度无关的惟一定价与保值策略。本文首先引入这种不完备市场模型，并运用梯度算子方法，得到一类相当广泛的衍生证券的定价与保值计算方法，作为两个应用例子，分别给出了组合型欧式期权及股票指数期权的定价与保值闭式解。
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| 关 键 词： | 不完备市场 定价与保值 梯度算子 应用例子 闲式解 |
| 文章编号： | 1001-4098（2007）09-0022-04 |
| 修稿时间： | 2007-02-20 |
The Valuation and Hedging of Some Derivatives under Incompleteness |
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| QIN Guo-wen,YANG Zhao-jun.The Valuation and Hedging of Some Derivatives under Incompleteness[J].Systems Engineering,2007,25(9):22-25. |
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| Authors: | QIN Guo-wen YANG Zhao-jun |
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| Institution: | 1. Hunan Academy of Social Sciences,Changsha 410003,Chinal 2. School of Economics and Trade,Hunan University,Changsha 410079,Chinal 3. School of Mathematics,Hunan University,Changsha 410079 ,China |
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| Abstract: | The valuation and hedging are relevant to the attitude of investors under incomplete market. The model studied here is a generalized B-S model. It appears that there are many replicable derivatives even under incompleteness. This paper obtains a sufficient condition for replicable derivative securities under an incomplete market, and utilizes the Gradient operator method to derive their valuation and hedging. Furthermore, as two examples, the paper acquires the closed-form solutions to the valuation and hedging for combined European option and stock index option. |
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| Keywords: | Incompleteness Valuation and Hedging Gradient Operator Examples Closed Solution |
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