Mathematical and data-driven modelling of multi-asset markets

虽然金融领域的大部分数学模型侧重于单一资产市场的详细分析模型，但大多数应用程序涉及多资产市场，通常涉及大量资产。这导致了许多与可伸缩性、模型稀疏性和套利约束相关的理论和计算挑战。这一研究项目的目的是为可扩展到高维环境的多资产金融市场开发有效的分析和数据驱动的建模方法和算法。研究项目将集中在四个方面：1.发展期权市场的无套利模拟方法。2.多资产交易策略的分析与风险监控。3.多资产市场的微观结构模型。4.以数据为导向的对冲和风险管理方法。我们的方法将把分析方法和随机建模与数据驱动的方法结合起来，基于使用新的计算方法，如生成性对抗网络(GAN)[1]和签名方法[3]来解决这些问题。这项研究项目解决了金融机构、风险管理者和市场监管机构面临的各种挑战。将特别关注算法和实施方面，以及使用市场数据的案例研究。应用将侧重于分析和模拟涉及期权和其他波动率合约的策略[4]。该项目与EPSRC的以下研究领域保持一致：(1)机器学习、深度学习和以数据为中心的建模；(2)统计学和应用概率；(3)数学建模；(4)运筹学。该项目将与法国巴黎银行合作完成。[1]古德费罗、伊恩、让·普盖-阿巴迪、迈赫迪·米孜、徐冰、大卫·沃德-法利、谢吉尔·厄扎尔、亚伦·库维尔和约书亚·本吉奥。“生成性对抗性网络。”ACM 63，第11期通讯(2020)：139-144。[2]Buehler、Hans、Lukas Gonon、Josef Teichmann和Ben Wood。“深度对冲。”《量化金融19》第8期(2019)：1271-1291。[3]Gyurkó，L.G.，Lyons，T.，Kontkowski，M.，&field，J.(2013)。从金融数据流的签名中提取信息。Arxiv预印本arxiv：1307.7244。[4]Cont，Rama，JoséDa Fonseca“隐含波动率表面的动态。”《量化金融2》，第1期(2002)：45。

While the bulk of mathematical models in finance has focused on detailed analytical models of single-asset markets, the majority of applications are concerned with multi-asset markets, often with a large number of assets. This leads to many theoretical and computational challenges related to scalability, model sparsity, and arbitrage constraints. The aim of this research project is to develop efficient analytical and data-driven modelling approaches and algorithms for multi-asset financial markets which are scalable to high-dimensional settings. The research project will focus on four directions: 1. Development of arbitrage-free simulation methods for options markets. 2. Analysis and risk monitoring of multi-asset trading strategies. 3. Microstructural modelling of multi-asset markets. 4. Data-driven approaches for hedging and risk management. Our methodology will combine analytical methods and stochastic modelling with data-driven approaches based on the use of novel computational methods such as Generative adversarial networks (GAN) [1] and the Signature method [3] to tackle these problems. This research project addresses various challenges faced by financial institutions, risk managers, and market regulators. Special attention will be devoted to algorithmic and implementation aspects, and case studies using market data. Applications will focus on the analysis and simulation of strategies involving options and other volatility contracts [4]. The project is aligned with the following EPSRC research areas: (1) machine learning, deep learning, and data-centric modelling (2) statistics and applied probability, (3) mathematical modelling, (4) operational research. This project will be done in partnership with BNP Paribas. [1] Goodfellow, Ian, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. "Generative adversarial networks." Communications of the ACM 63, no. 11 (2020): 139-144. [2] Buehler, Hans, Lukas Gonon, Josef Teichmann, and Ben Wood. "Deep hedging." Quantitative Finance 19, no. 8 (2019): 1271-1291. [3] Gyurkó, L. G., Lyons, T., Kontkowski, M., & Field, J. (2013). Extracting information from the signature of a financial data stream. arXiv preprint arXiv:1307.7244. [4] Cont, Rama, and José Da Fonseca. "Dynamics of implied volatility surfaces." Quantitative finance 2, no. 1 (2002): 45.