Statistics and Finance

统计与金融

• 批准号: 9971738
• 负责人: Per Mykland
• 金额: $ 27万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-15 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971738&HistoricalAwards=false
• 关键词: Statistics; Finance

9971738It is proposed to continue the research initiated by the P.I. on how to use confidence and prediction sets for stochastic differential equations to set hedging strategies for derivative securities. The study will investigate both the statistical methods used to set such sets, and how to trade for a given set. The plan is to compare sets based purely on nonparametric prediction with those based on confidence statements, and also to look at hybrid methods, involving neighborhoods of parametric models. The latter will also provide guidance on how to conduct model selection in such circumstances. Several inference methods will be investigated, ranging from excursion based methods to profile likelihood. In terms of the interface between sets and trading algorithms, it is proposed to extend the present theory to non-European options. It is also the plan to investigate the multiple comparison issues that arise if one wishes to revise prediction intervals in the course of a trading strategy. Finally, it is the intention to look into alternative models to stochastic differential equations, models that can be used for hedging and that are closer to the data than continuous processes. Derivative securities -- options, futures, and similar instruments -- have emerged as a major feature of the contemporary economic environment. They are a versatile and efficient mechanism for trading risk, thus lowering its cost. There is, however, a dark side to derivatives, in that it can be hard to assess the real risks involved. This is not only the case for `naive' market participants, as evidenced by a number of incidents involving major financial institutions. These difficulties are, to an important extent, caused by the absence of a connection between statistical methods and the evaluation of financial risk. There is a substantial literature on the statistical analysis of financial data. Apart from short-term considerations, however, there is little knowledge on how to use statistical results based on historical data to quantify the risks associated with derivatives. The aim of this project is to change this situation by providing ways of tying up statistical results and the trading strategies on which the values of derivative securities depend. This will provide ways of setting contingency reserves and fallback liquidation strategies without interfering in the day-to-day operation of the financial institutions trading in options.

9971738建议继续由私人投资局就如何利用随机微分方程的置信度和预测集为衍生证券设定套期保值策略的研究。这项研究将调查用于设置此类集合的统计方法，以及如何交易给定的集合。我们的计划是将纯粹基于非参数预测的集合与基于置信度声明的集合进行比较，并研究涉及参数模型邻域的混合方法。后者还将就如何在这种情况下进行模式选择提供指导。将研究几种推断方法，从基于漂移的方法到轮廓似然方法。在集合和交易算法之间的接口方面，建议将目前的理论扩展到非欧式期权。它还计划调查出现的多重比较问题，如果一个人希望修改交易策略过程中的预测区间。最后，它的目的是寻找随机微分方程的替代模型，这些模型可以用于套期保值，并且比连续过程更接近数据。衍生证券--期权、期货和类似工具--已成为当代经济环境的一个主要特征。它们是一种多功能而高效的交易风险机制，从而降低了风险成本。然而，衍生品也有阴暗面，因为它可能很难评估所涉及的真正风险。这不仅仅是“幼稚”的市场参与者的情况，涉及主要金融机构的一些事件证明了这一点。这些困难在很大程度上是由于统计方法与金融风险评估之间缺乏联系造成的。关于金融数据的统计分析，有大量的文献。然而，除了短期考虑外，对于如何利用基于历史数据的统计结果来量化与衍生品相关的风险，人们几乎没有什么了解。这个项目的目的是通过提供将统计结果和衍生品证券价值所依赖的交易策略捆绑在一起的方法来改变这种情况。这将提供制定应急准备金和后备清算战略的方法，而不会干扰进行期权交易的金融机构的日常运作。