Statistics and Finance

9971738本文提出继续前人关于如何利用随机微分方程的置信度和预测集来设置衍生证券套期保值策略的研究。该研究将调查用于设置这些集合的统计方法，以及如何为给定集合进行交易。计划是比较纯粹基于非参数预测的集合和那些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。后者也将为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，从基于偏移的方法到剖面似然。在集和交易算法之间的接口方面，提出将该理论扩展到非欧式期权。该计划还将调查在交易策略过程中，如果希望修改预测区间时出现的多重比较问题。最后，它的目的是研究随机微分方程的替代模型，这些模型可以用于对冲，并且比连续过程更接近数据。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高效的风险交易机制，从而降低了风险交易的成本。然而，衍生品也有不好的一面，因为很难评估所涉及的实际风险。这不仅仅是“天真”的市场参与者的情况，一些涉及大型金融机构的事件就证明了这一点。这些困难在很大程度上是由于统计方法与财务风险评价之间缺乏联系造成的。关于财务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。这个项目的目的是通过提供将统计结果和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。这将提供在不干扰从事期权交易的金融机构的日常运作的情况下，设定应急准备金和备用清算策略的方法。

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.