  The use of machine learning to generate synthetic data has grown in
popularity with the proliferation of text-to-image models and especially large
language models. The core methodology these models use is to learn the
distribution of the underlying data, similar to the classical methods common in
finance of fitting statistical models to data. In this work, we explore the
efficacy of using modern machine learning methods, specifically conditional
importance weighted autoencoders (a variant of variational autoencoders) and
conditional normalizing flows, for the task of modeling the returns of
equities. The main problem we work to address is modeling the joint
distribution of all the members of the S&P 500, or, in other words, learning a
500-dimensional joint distribution. We show that this generative model has a
broad range of applications in finance, including generating realistic
synthetic data, volatility and correlation estimation, risk analysis (e.g.,
value at risk, or VaR, of portfolios), and portfolio optimization.
