Robust option pricing with Neural SDEs

使用神经 SDE 进行稳健的期权定价

• 批准号: 2280357
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2280357
• 关键词: Robust; option; pricing; Neural; SDEs

1. Introduction: Mathematical modelling is ubiquitous in the financial industry and drives key decision processes. Every model provides only a crude approximation to reality and the risk of using an inadequate model is usually hard to detect and quantify. Model uncertainty is, hence, an essential part of mathematical modelling and is particularly important in mathematical finance and economics, where one cannot base models on well-established physical laws. Nevertheless, standard modelling practices in finance rarely address this model uncertainty. One such paradigm, where the model risk is central to its philosophy, is the robust finance approach. Currently, machine learning techniques are opening doors to different ways of robust and data-driven model selection mechanisms. However, most machine learning models are still considered to be so-called "black-boxes" as individual parameters do not have meaningful interpretation. We therefore plan to focus on combining classical modelling with deep learning techniques in the context of option pricing. Until recently, model complexity was undesirable, amongst other reasons, for increasing the computational effort required to perform, in particular calibration, but also pricing and risk calculations. With greater uptake of machine learning methods and greater computational power more complex models can now be used. In our approach, we let the data dictate the model, while still keeping a strong prior on the model form. This is achieved by using stochastic differential equations (SDEs) for the model dynamics, but instead of choosing a fixed parametrization for the model SDEs we allow the drift and diffusion to be given by over-parametrised neural networks. We refer to these as Neural SDEs. These are shown to not only provide a systematic framework for model selection, but also, quite remarkably, to produce robust estimates on the derivative prices. Here, the calibration and model selection are done simultaneously. Since the neural SDE model is overparametrised, there is a large pool of possible models and the training algorithm selects a model. 2. Alignment to EPSRC research areas: This project falls within the EPSRC 'Statistics and applied probability' research area. Presented methodology combines classical probabilistic techniques from stochastic and probabilistic modelling and novel machine learning approaches from data-science, more specifically -- deep neural networks. We kept our focus on applied probability in combination with robust statistics and artificial intelligence, which is in line with the proposed research area. We emphasise this approach has applications well beyond just option pricing and, more broadly, finance. It covers any scenario including modelling processes with inherit randomness and known values or measurements (or functions thereof) at different points in time. Such applications include problems in data analytics, healthcare modelling and medical statistics, artificial intelligence and uncertainty quantification etc.3. Collaboration: The project was carried out jointly with the Alan Turing Institute (ATI) and University of Edinburgh, more particularly with David Siska and the Programme Director for Finance and Economics at ATI, Lukasz Szpruch and members of his research team Marc Sabate Vidales and Patryk Gierjatowicz.

1.简介：数学建模在金融行业中无处不在，并驱动着关键的决策过程。每个模型仅提供对现实的粗略近似，并且使用不适当模型的风险通常难以检测和量化。因此，模型不确定性是数学建模的重要组成部分，在数学金融和经济学中尤其重要，因为在这些领域，模型不能建立在完善的物理定律的基础上。然而，金融领域的标准建模实践很少解决这种模型的不确定性。其中一种范式是稳健的财务方法，其中模型风险是其理念的核心。目前，机器学习技术正在为不同方式的稳健和数据驱动的模型选择机制打开大门。然而，大多数机器学习模型仍然被认为是所谓的“黑匣子”，因为单个参数没有有意义的解释。因此，我们计划专注于在期权定价的背景下将经典模型与深度学习技术相结合。直到最近，模型复杂性仍然是不受欢迎的，其中一个原因是增加了执行（特别是校准）以及定价和风险计算所需的计算工作量。随着机器学习方法的广泛采用和计算能力的增强，现在可以使用更复杂的模型。在我们的方法中，我们让数据决定模型，同时仍然保持模型形式的强大先验。这是通过使用模型动力学的随机微分方程 (SDE) 来实现的，但我们不是为模型 SDE 选择固定参数化，而是允许由过参数化神经网络给出漂移和扩散。我们将这些称为神经 SDE。事实证明，这些不仅为模型选择提供了系统框架，而且非常引人注目的是，可以对衍生品价格进行稳健的估计。在这里，校准和模型选择是同时完成的。由于神经 SDE 模型过度参数化，因此存在大量可能的模型，并且训练算法会选择一个模型。 2. 与 EPSRC 研究领域的一致性：该项目属于 EPSRC“统计和应用概率”研究领域。所提出的方法结合了随机和概率建模的经典概率技术以及数据科学（更具体地说是深度神经网络）的新颖机器学习方法。我们将重点放在应用概率与稳健的统计和人工智能的结合上，这与拟议的研究领域是一致的。我们强调这种方法的应用远远超出了期权定价以及更广泛的金融领域。它涵盖了任何场景，包括具有继承随机性和不同时间点的已知值或测量值（或其函数）的建模过程。这些应用包括数据分析、医疗保健建模和医学统计、人工智能和不确定性量化等方面的问题3。合作：该项目是与艾伦图灵研究所 (ATI) 和爱丁堡大学联合开展的，特别是与 David Siska 以及 ATI 金融和经济项目总监 Lukasz Szpruch 及其研究团队成员 Marc Sabate Vidales 和 Patryk 合作开展吉尔贾托维奇。