In the financial services industry, forecasting the risk factor distribution
conditional on the history and the current market environment is the key to
market risk modeling in general and value at risk (VaR) model in particular. As
one of the most widely adopted VaR models in commercial banks, Historical
simulation (HS) uses the empirical distribution of daily returns in a
historical window as the forecast distribution of risk factor returns in the
next day. The objectives for financial time series generation are to generate
synthetic data paths with good variety, and similar distribution and dynamics
to the original historical data. In this paper, we apply multiple existing deep
generative methods (e.g., CGAN, CWGAN, Diffusion, and Signature WGAN) for
conditional time series generation, and propose and test two new methods for
conditional multi-step time series generation, namely Encoder-Decoder CGAN and
Conditional TimeVAE. Furthermore, we introduce a comprehensive framework with a
set of KPIs to measure the quality of the generated time series for financial
modeling. The KPIs cover distribution distance, autocorrelation and
backtesting. All models (HS, parametric and neural networks) are tested on both
historical USD yield curve data and additional data simulated from GARCH and
CIR processes. The study shows that top performing models are HS, GARCH and
CWGAN models. Future research directions in this area are also discussed.

金融服务行业中，根据历史和当前市场环境来预测风险因素分布是市场风险建模和风险价值 (VaR) 模型的关键。本研究应用多个现有的深度生成方法，如 CGAN、CWGAN、Diffusion 和 Signature WGAN，以及提出并测试两种新方法进行条件多步时间序列生成，即编码器 - 解码器 CGAN 和条件 TimeVAE。此外，我们引入了一个全面的框架和一组关键绩效指标 (KPIs)，用于衡量金融建模中生成时间序列的质量。KPIs 包括分布距离、自相关和回测。在历史美元收益曲线数据和从 GARCH 和 CIR 过程模拟的附加数据上测试了所有模型 (HS、参数模型和神经网络)。研究表明，HS、GARCH 和 CWGAN 模型是表现最好的模型。此领域中的未来研究方向也在研究中进行了讨论。

金融时间序列的深度生成建模与 VaR 应用：一项比较评述

Deep Generative Modeling for Financial Time Series with Application in  VaR: A Comparative Review

In the last five years, the financial industry has been impacted by the
emergence of digitalization and machine learning. In this article, we explore
two methods that have undergone rapid development in recent years: Gaussian
processes and Bayesian optimization. Gaussian processes can be seen as a
generalization of Gaussian random vectors and are associated with the
development of kernel methods. Bayesian optimization is an approach for
performing derivative-free global optimization in a small dimension, and uses
Gaussian processes to locate the global maximum of a black-box function. The
first part of the article reviews these two tools and shows how they are
connected. In particular, we focus on the Gaussian process regression, which is
the core of Bayesian machine learning, and the issue of hyperparameter
selection. The second part is dedicated to two financial applications. We first
consider the modeling of the term structure of interest rates. More precisely,
we test the fitting method and compare the GP prediction and the random walk
model. The second application is the construction of trend-following
strategies, in particular the online estimation of trend and covariance
windows.

本文探讨了高斯过程和贝叶斯优化这两种方法在金融建模中的应用，特别是在利率期限结构建模和趋势跟踪策略中的运用。