Statistics and Finance

9971738建议继续P.I.发起的研究。如何使用随机微分方程的置信集和预测集来设定衍生证券的对冲策略。 这项研究将调查用于设置这些集合的统计方法，以及如何交易给定的集合。 该计划是比较纯粹基于非参数预测的集合与基于置信度声明的集合，并研究混合方法，包括参数模型的邻域。 后者还将就如何在这种情况下进行模式选择提供指导。 将研究几种推理方法，从基于偏移的方法到配置文件的可能性。 在集合与交易算法的接口方面，本文提出将现有理论推广到非欧式期权。 这也是计划，以调查出现的多重比较问题，如果一个人希望在交易策略的过程中修改预测区间。 最后，它的目的是寻找替代模型的随机微分方程，模型，可用于对冲和更接近的数据比连续过程。 衍生证券--期权、期货和类似的工具--已经成为当代经济环境的一个主要特征。 它们是一种多功能和有效的风险交易机制，从而降低了成本。 然而，衍生品也有阴暗的一面，因为它可能很难评估所涉及的真实的风险。 正如涉及主要金融机构的一些事件所证明的那样，这不仅是“天真”的市场参与者的情况。 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。 有大量关于金融数据统计分析的文献。 然而，除了短期考虑之外，对于如何使用基于历史数据的统计结果来量化与衍生品相关的风险，人们知之甚少。 本项目的目的是通过提供将统计结果与衍生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。 这将提供在不干预从事期权交易的金融机构的日常运作的情况下设置应急储备和后备清算策略的方法。

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.