无套利均衡与风险中性假设在期权定价中的等价性

The relationship between no - arbitrage equilibrium and risk - neutral supposition in fixing a price of options

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。

No-arbitrage equilibrium and risk - neutral supposition take important stations during the process that we fix a price of options. But they seems to be thought two different suppositions with no relation. We can see from our paper that the two suppositions or methods are used together in the model's preconditions and the deducing process. Also we find the conclusions come from the two methods are properly the same. So the relationship between the two suppositions are the key to the options pricing problem. In our paper, we first enduce the question through B-S model; then give the definitions of no- arbitrage equilibrium and risk- neutral supposition. We then prove they two equivalent through Feynman- Kac formula and equivalent martingale measure. We at the end draw a conclusion: no - arbitrage equilibrium and risk - neutral supposition depend on each other for existence in the options pricing model.