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

利率是日常生活的一部分。它们是经济中金融资源配置的基础，因此对经济运行的几乎每一个方面都有深远的影响，从消费者支出到企业生产到金融投资，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，这些资产的价值至关重要。因此，了解短期利率动态是目前学术界和实践者关注的主要问题。对短期利率进行建模的最大挑战是在捕捉利率动态的复杂特征时追求灵活性和在模型的实施中追求可跟踪性和效率之间的两难境地。文献中现有的方法通常要么不能充分解释短期汇率动态，要么在以方便和信息丰富的方式从数据中得出推论方面缺乏效率。因此，本项目的总体目标是开发一种灵活有效的基于可能性的利率动态建模新方法。具体而言，本项目旨在为一类随机微分方程提出灵活的非参数规范，并开发基于似然的推理程序，并在此背景下研究非参数效率。它还打算将这种方法扩展到多变量情况，并测试新方法在一系列以利率为特征的实质性经验问题中的适用性和适宜性。该项目具有一系列创新的方法、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，这里提倡的使用非参数rsde的方法是全新的，并且填补了仍然由参数方法主导的文献中的实质性空白。在这种情况下使用经验似然也是新颖的。鉴于涉及利率的经验问题范围广泛，本建议中开发的方法也将为该学科的重大经验贡献提供广泛的范围。虽然所提出的方法是在利率建模的背景下发展起来的，但它的普遍性足以在广泛的随机分析领域产生方法论上的影响，对统计学、物理学、工程学、化学、医学等非经济学科具有实质性的适用性。

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.