Modelling Interest Rate Dynamics: A Flexible and Efficient Nonparametric Likelihood Approach

利率是日常生活的一部分。利率是经济中金融资源分配的基础，因此对经济运行的几乎每一个方面都有深远的影响，从消费支出到企业生产，再到金融投资，以及就业，通货膨胀和增长。期限少于一年的债务工具的利率被称为短期利率。在金融市场的背景下，短期利率的动态对所有经济和金融资产的估值至关重要，这些资产的价值在很大程度上取决于它们。因此，理解短期利率动态是目前学术界和实务界关注的主要问题，短期利率模型的最大挑战是在追求捕捉利率动态复杂特征的灵活性和实现模型的易处理性和效率之间的两难选择。现有的方法在文献中通常不能充分考虑短期利率动态或缺乏效率，从数据中得出的推论的方式是方便和informations.Thus，本项目的总体目标是开发一个灵活和高效的新的基于似然模型的方法来建模利率动态。具体来说，这个项目的目的是提出一个灵活的非参数规范的一类随机微分方程，并开发基于似然推理程序，并调查在这种情况下的非参数效率。本项目旨在将该方法扩展到多变量情形，并在一系列具有利率特征的实质性实证问题中检验新方法的适用性和适用性，该项目以其一系列创新的方法论、理论和实证建议，有望在利率建模方面取得新的进展。至关重要的是，这里提倡使用非参数RSDES的方法是全新的，填补了文献中仍然由参数方法主导的重大空白。在这种情况下使用经验似然法也是新颖的。考虑到利率所涉及的广泛的实证问题，本提案中开发的方法也将为该学科的重大实证贡献提供广泛的范围。尽管所提出的方法是在利率建模的背景下开发的，但它足够普遍，可以在随机分析的广泛领域产生方法学影响，具有对非经济学科如统计学、物理学、工程学、化学、医学科学等的实质性适用性。

Interest rates are a part of everyday life. They are fundamental in the allocation of financial resources in the economy and hence have profound implications on almost every aspect of its operation, from consumer spending to firm production to financial investments, as well as on employment, inflation, and growth.Interest rates on debt instruments having maturities of less than one year are known as short term interest rates. In the context of financial markets, the dynamics of short term interest rates are central to the valuation of all economic and financial assets whose values crucially depend on them. Therefore, understanding short term interest rate dynamics is now a major concern of both academics and practitioners.The greatest challenge in modeling short term interest rates is the dilemma between the quest for flexibility in capturing complex features of interest rate dynamics and the desire for tractability and efficiency in the implementation of the model. Existing methods in the literature generally either fail to account for short rate dynamics adequately or lack efficiency in drawing inferences from data in a manner that is convenient and informative.Thus the overall objective of this project is to develop a flexible and efficient new likelihood based approach for modeling interest rate dynamics. Specifically, this project aims to propose a flexible nonparametric specification for a class of stochastic differential equations and develop likelihood based inferential procedures and investigate nonparametric efficiency in that context. It also intends to extend the approach to multivariate case and test the applicability and suitability of the new methodology in a range of substantive empirical problems in which interest rates feature.This project, with its range of innovative methodological, theoretical and empirical proposals, promises new advances on the interest rate modeling front. Crucially, the approaches advocated here for using nonparametric RSDEs are completely new, and fill a substantial gap in a literature still dominated by parametric approaches. The use of Empirical Likelihood in this context is also novel. The methodology developed in this proposal will also provide extensive scope for significant empirical contributions to the discipline, given the wide range of empirical problems in which interest rates are concerned.Although the proposed approach is developed in the context of interest rate modeling, it is general enough to have a methodological impact in the broad realm of stochastic analysis, with substantial applicability to non-economic disciplines such as statistics, physics, engineering, chemistry, medical science, and so on.