Statistics and Finance

点击翻译按钮获取中文摘要

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.