Abstract
The thesis investigates high dimensional financial system modelling, which is important in today's digital age where multi-dimensional data is widely used in finance and data science research. Two case studies which are popular and well-researched in the recent financial market, multi-dimensional option pricing, together with high-dimensional sectors analysis, are taken as examples for demonstration, respectively. The first chapter of this thesis gives an introduction and a thorough literature review of high-dimensional modelling in the example financial systems. The detailed investigation and experiments are discussed in the subsequent chapters.In the case of option pricing problem, due to the complexity of the multi-dimensional Black-Scholes equations and the formulation of boundary conditions, stable and accurate results for multi-asset option pricing problems can be hard to achieve via some classical popular used numerical methods. Therefore, a newly derived General Finite Integration Method, which elaborates the idea of the Finite Integration Method (FIM), has been introduced. In GFIM formulation, we define the approximant using the piecewise polynomial approximation and provide the transformation of differential operators of governing equation into an integration matrix through unrestricted nodal point collocation. GFIM, or incorporated with Domain Decomposition Technique in Space-Time (GFIM-ST), have demonstrated the flexibility and stability of solving multi-dimensional partial differential equations in numerical experiments. Several numerical examples of solving free-boundary American option and two-assets exchange options pricing problems have been discussed to show the advantage of GFIM.
In the financial sectors case study, two sectors are considered: traditional stock sectors and cryptocurrency categories. The study explores the interdependence between asset classes belonging to different groups, which may be hard to detect due to potential sparsity within the system. The Sparse Network Model (SNM) has been extended for the estimator to identify influential cryptocurrencies and sectors. The oracle properties of the estimator have been proved, and the model's performance has been validated in extensive synthetic data experiments.
In the stock sector analysis, the S\&P100 index with 11 sectors in 2021-2023 is studied based on 5-min frequency data. SNM models have identified leading stocks for each sector, which are more frequent than benchmark models and supported by news on the corresponding date. In the crypto study, 55 cryptocurrency sectors and highly capitalized cryptocurrencies during 2015-2020 have been included in the real data test. The results show that different coins or categories stand out as influences during different market stages, with Bitcoin still playing an important role despite the market entering a new stage.
| Date of Award | 21 Jun 2023 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Yiu Chung Benny HON (Supervisor) & Wonjung LEE (Supervisor) |