不完备市场下一类衍生证券的无风险定价与保值

The Valuation and Hedging of Some Derivatives under Incompleteness

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。

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.