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

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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.