Is Deliberate Misspecification Desirable? Statistical Study of Financial and Other Time-Dependent Data

自从17世纪统计和概率发明以来，赌博一直是理解统计和概率概念的主要来源之一。遵循这一传统，在许多方面类似于赌博的应用的基础上，追求统计思想和结果的发展。该应用程序是衍生证券，如期权。在待调查的概念性问题中，有两个主题反复出现。一个是需要将统计推断与应用程序的需求集成在一起。另一个原因是，这种需求经常导致故意错误指定模型，超出了普通统计中通常出现的情况。这个建议也是关于应用的。期权交易与赌博的不同之处在于其对经济的重要性，以及（大多数时候）其社会价值。这也是一个错误和理解不足可能导致社会其他部分遭受重大灾难的行业。该项目的主要目标之一是提高对期权交易中涉及的（数据）过程的理解，并促进政府监管。双重意图是统计概念的发展和对当代经济主要部门的研究。这两个目标结合在一起的原因是，统计数据与衍生品行业目前面临的三个最重大的问题有关。一个是普遍未能将统计结果纳入定价、交易和监管决策。另一个是证券价格的巨大不连续性（由于各种冲击或仅仅是内生的跳跃）的影响。最后，期权值的设置经常缺乏透明度。这些是需要回答的应用问题。监管机构和金融机构都对这三个难题非常感兴趣。这个项目的成果应该对经济有广泛的帮助，既有利于衍生品的消费者，也有利于试图监管这个从外部看不透明的行业的政府。这些问题也经常反映在公司治理的设置上。在理论方面，提议的项目是一个扭曲的统计推断，因为目标是采取应用程序并将其与推理过程相结合。由于推理将针对纵向数据，例如扩散和跳跃扩散，因此结论也将为此类数据的一般推理提供见解。该项目的一个主要论点是，从数据分析到实际交易和监管的链条，最好通过分解其不同的环节来研究。然后可以分别研究它们，通常使用不同的方法和故意不同的模型规范，或者经常使用有用的错误规范。这样就可以把这些联系孤立起来，从而使综合分析极不合理。它还使其他的联系更加透明，这些联系可以进行可靠的分析。从统计和财务的角度来看，这种为不同目的使用不同工具的意愿似乎相当成功。一个主要的例子是扩散的方差分析（ANOVA）。这一装置使交易能够以比单独校准或建模更复杂的方式适应市场。

AbstractDMS-0204639PI: Per MyklandGambling has been one of the main sources for conceptual understanding of statistics and probability, ever since the invention of the latter in the 1600s. Following this tradition, the development of ideas and results in statistics is pursued, on the basis of an application that resembles gambling in many respects. The application is derivative securities such as options. Among the conceptual issues to be investigated, two stand out as recurring themes. One is the need to integrate statistical inference with the needs of the application. The other is that this need often leads to deliberately misspecified models, beyond what is usually the case in ordinary statistics. This proposal is also about the application. Options trading differs from gambling both in its importance to the economy, and (most of the time) in its social value. It is also an industry where mistakes and insufficient understanding can lead to substantial calamity for the rest of society. One of the primary goals of this project is to improve understanding of the (data) processes involved in options trading, and to facilitate government regulation. The dual intentions are conceptual development in statistics and the study of the major sectors of contemporary economy.The reason why these two aims go together is that statistics relates to three of the most substantial problems facing the derivatives industry today. One is the common failure to incorporate statistical findings into decisions of pricing, trading and regulation. Another is the effect of big discontinuities (jumps, due to various shocks, or simply endogenous) in the prices of securities. And, finally, the frequent lack of transparency in the setting of options values. These are the applied questions to be answered. The three difficulties are of keen interest to regulators and financial institutions alike. Results from the project should be broadly useful to the economy, benefiting both consumers of derivatives and governments trying to regulate a business that is opaque from the outside. The problems are also often mirrored in the setting of corporate governance. On the theoretical side, the proposed project is about statistical inference with a twist, in that the goal is to take the application and integrate it with the process of inference. Since inference will be for longitudinal data, such as diffusions and jump diffusions, the conclusions will also give insights to general inference for such data. A main contention of the project is that the chain from data analysis to actual trading and regulation is best studied by taking apart its different links. These can then be studied separately, often with different methods and deliberately different model specifications, or frequently even useful misspecifications. This permits the isolation of those links, which makes an integrated analysis quite ill posed. And it gives greater transparency to those other links, which are amenable to a reliable analysis. This willingness to use separate tools for separate purposes appears to be quite successful, both from a statistical and a financial perspective. A main example is the analysis of variance (ANOVA) for diffusions. This device leads to trading that can adapt to the markets in more sophisticated ways than by calibration or modeling alone.