Modern financial markets are highly interconnected and exhibit a diverse range of non-linear behaviors such as time-varying volatility. Financial econometric models designed to gain insight into such markets must be able to reproduce such non-linear stylized facts, and thereby renders conventional linear econometric models such as linear regression models obsolete for this purpose. Moreover, the interconnectedness necessitates the joint modeling of many assets at the same time, thereby requiring both large data sets of and large-scale models that can capture dependencies between many assets.
With large-scale non-linear econometric models comes the need for numerical methods for fitting the models with data. With current numerical methods, a high degree of expertise, substantial development efforts and large amounts of computing power is required to fit each particular model instance to data. Such models might require days of computing time and many weeks of programming and development effort. This project seeks to develop new such numerical methods that are easy to use by non-experts in computational methods and at the same time are computationally fast and reliable. The development of such methods would allow practitioners to build and refine a steady stream of models, and in particular models that captures the finer detail of the phenomena studied. Through the development of easy to use- and open access software, the overarching aim of the project, to “democratize” the access to the benefit of such models will be realized.
The project is highly cross-disciplinary in nature. It brings together experienced researchers with backgrounds in economics, econometrics and mathematical statistics, and aims to train a less experience colleague towards a PhD.
The modern financial system generates continuously larger amounts of data. Enabling the analysis of such data sets may bring substantial benefit to society in the form of better understanding of how financial markets function.
Modern Bayesian econometrics relies on numerical algorithms for fitting models to data. With the growth of both amounts and complexity of data sets, and correspondingly complicated Bayesian hierarchical dynamic models comes the demand for ever more capable such numerical algorithms.
To this end, the project seeks to develop a new such algorithms based on a particular class of continuous time stochastic processes: Generalized Randomized Hamiltonian Monte Carlo (GRHMC) processes. Such processes have many interesting, rather surprising and empirically useful properties.
A large class of such processes with the correct target distribution may be constructed. The first part of the project is devoted to finding the best possible members of this class for Bayesian hierarchical econometric models. In particular, this part would involve the development of a new metric tensor for Riemannian GRHMC processes that is especially targeted for hierarchical econometric models.
Secondly, the project will consider the application of the developed methodology in large scale models within macroeconomics, conventional financial markets and commodity finance. These will serve both as test cases/illustrations of the developed methodology and also warrant their own free-standing publications in economics/finance oriented journals.
Further outputs, in the form of easy-to-use software, of a successfully executed project would enable researchers and practitioners to routinely build such more realistic models, which would subsequently lead to further insights into the workings of the financial system.
The project will involve a diverse array of researchers with background from economics/econometrics and mathematical statistics, and will also train 1 PhD student.