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期权定价公式的模型推导中,无套利均衡与风险中性假设占有重要地位。不过它们似乎一直以来都被认为两个分离的假设,并没有什么关系。但这两种假设或者说方法要么同时出现在模型的前提和推导过程中交替应用,要么可以用两种方法来推导出同样的结论。那么两者之间的关系便成为可以在期权定价问题中同时应用这两种方法的一个关键。在这篇论文开始,我们通过B-S模型的推导发现到这个问题。随之便在论文中详细阐述了无套利均衡与风险中性假设,并指出且证明了它们之间在期权定价问题中存在的等价关系。其方法则主要是从利用Feynman-Kac公式和引入等价鞅测度两个不同的方面来说明无套利均衡和风险中性假设的等价关系。最后我们以二叉树模型为例子详细验证了论文中提出的这个论点。从而最终得出了我们的结论:在期权定价模型中的这个曾被认为没有什么关系的两个假设条件存在着相对严谨的依存关系。
In the model derivation of option pricing formula, no arbitrage equilibrium and risk neutral assumption occupy an important position. However, it seems that they have always been regarded as two separate assumptions and have nothing to do with them. However, both of these assumptions or approaches occur either simultaneously in the model’s premise and in the derivation process, or they can be derived in two ways. Then the relationship between the two becomes one of the keys to applying both approaches in the option pricing problem. At the beginning of this paper, we found this problem through the derivation of the B-S model. Subsequently, this paper elaborates the hypothesis of no arbitrage equilibrium and risk neutrality in the paper, and points out and proves the equivalence relationship between them in option pricing. The method is mainly to explain the equivalence relation between arbitrage-free equilibrium and risk-neutral assumption from the two different aspects of using Feynman-Kac formula and introducing the equivalent martingale measure. Finally, we use the binary tree model as an example to verify the thesis proposed in this thesis. Finally, we come to the conclusion that the two hypothetical conditions in the option pricing model that have been considered as nonexistent have relatively strict dependencies.