A note on the use of fractional Brownian motion for financial modeling
A note on the use of fractional Brownian motion for financial modeling
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DOI：
10.1016/j.econmod.2012.09.003
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发表时间：
2013
影响因子：
4.7
通讯作者：
S. Rostek;R. Schöbel
中科院分区：
文献类型：
--
作者：
S. Rostek;R. Schöbel
在过去十年的后半段，分数布朗运动在金融模型中的应用停滞不前。分数布朗运动的有利的时间序列性质表现出长期依赖性，但同时也伴随着一个明显无法克服的缺点：套利的存在。在过去的两年中，已经发表了几个使用分数布朗运动的新模型。然而，从经济学的角度来看，这些模式是否是合理的选择，这个问题仍然没有得到解决。在本文中，我们采用了一个简单的数学论证，以澄清分数布朗运动何时以及为什么适合于经济建模：我们提供了一个分数模拟Sethi和Lehoczky（1981）的工作，从而确认分数布朗运动和连续可交易性是不相容的。从分数布朗运动的市场微观结构角度来看，分数布朗运动的正确使用本质上意味着动态市场的不完全性。建立应用的桥梁，我们表明，一个特殊的，但仍然流行的结果，在部分期权定价的文献可以很好地解释的事实，作者不遵守这种需要的兼容性。
In the second part of the past decade, the usage of fractional Brownian motion for financial models was stuck. The favorable time-series properties of fractional Brownian motion exhibiting long-range dependence came along with an apparently insuperable shortcoming: the existence of arbitrage. Within the last two years, several new models using fractional Brownian motion have been published. However, still the problem remains unsolved whether such models are reasonable choices from an economic perspective. In this article, we take on a straightforward mathematical argument in order to clarify when and why fractional Brownian motion is suited for economic modeling: We provide a fractional analog to the work of Sethi and Lehoczky (1981) thereby confirming that fractional Brownian motion and continuous tradability are incompatible. In the light of a market microstructure perspective to fractional Brownian motion, it becomes clear that the correct usage of fractional Brownian motion inherently implies dynamic market incompleteness. Building a bridge to application, we show that one peculiar, but nevertheless popular result in the literature of fractional option pricing can be well explained by the fact that authors disobeyed this need for compatibility.