Diffusion Models

Beyond Monte Carlo: Harnessing Diffusion Models to Simulate Financial Market Dynamics ArXiv ID: 2412.00036 “View on arXiv” Authors: Unknown Abstract We propose a highly efficient and accurate methodology for generating synthetic financial market data using a diffusion model approach. The synthetic data produced by our methodology align closely with observed market data in several key aspects: (i) they pass the two-sample Cramer - von Mises test for portfolios of assets, and (ii) Q - Q plots demonstrate consistency across quantiles, including in the tails, between observed and generated market data. Moreover, the covariance matrices derived from a large set of synthetic market data exhibit significantly lower condition numbers compared to the estimated covariance matrices of the observed data. This property makes them suitable for use as regularized versions of the latter. For model training, we develop an efficient and fast algorithm based on numerical integration rather than Monte Carlo simulations. The methodology is tested on a large set of equity data. ...

Generation of synthetic financial time series by diffusion models ArXiv ID: 2410.18897 “View on arXiv” Authors: Unknown Abstract Despite its practical significance, generating realistic synthetic financial time series is challenging due to statistical properties known as stylized facts, such as fat tails, volatility clustering, and seasonality patterns. Various generative models, including generative adversarial networks (GANs) and variational autoencoders (VAEs), have been employed to address this challenge, although no model yet satisfies all the stylized facts. We alternatively propose utilizing diffusion models, specifically denoising diffusion probabilistic models (DDPMs), to generate synthetic financial time series. This approach employs wavelet transformation to convert multiple time series (into images), such as stock prices, trading volumes, and spreads. Given these converted images, the model gains the ability to generate images that can be transformed back into realistic time series by inverse wavelet transformation. We demonstrate that our proposed approach satisfies stylized facts. ...

FinDiff: Diffusion Models for Financial Tabular Data Generation ArXiv ID: 2309.01472 “View on arXiv” Authors: Unknown Abstract The sharing of microdata, such as fund holdings and derivative instruments, by regulatory institutions presents a unique challenge due to strict data confidentiality and privacy regulations. These challenges often hinder the ability of both academics and practitioners to conduct collaborative research effectively. The emergence of generative models, particularly diffusion models, capable of synthesizing data mimicking the underlying distributions of real-world data presents a compelling solution. This work introduces ‘FinDiff’, a diffusion model designed to generate real-world financial tabular data for a variety of regulatory downstream tasks, for example economic scenario modeling, stress tests, and fraud detection. The model uses embedding encodings to model mixed modality financial data, comprising both categorical and numeric attributes. The performance of FinDiff in generating synthetic tabular financial data is evaluated against state-of-the-art baseline models using three real-world financial datasets (including two publicly available datasets and one proprietary dataset). Empirical results demonstrate that FinDiff excels in generating synthetic tabular financial data with high fidelity, privacy, and utility. ...

Diffusion Variational Autoencoder for Tackling Stochasticity in Multi-Step Regression Stock Price Prediction ArXiv ID: 2309.00073 “View on arXiv” Authors: Unknown Abstract Multi-step stock price prediction over a long-term horizon is crucial for forecasting its volatility, allowing financial institutions to price and hedge derivatives, and banks to quantify the risk in their trading books. Additionally, most financial regulators also require a liquidity horizon of several days for institutional investors to exit their risky assets, in order to not materially affect market prices. However, the task of multi-step stock price prediction is challenging, given the highly stochastic nature of stock data. Current solutions to tackle this problem are mostly designed for single-step, classification-based predictions, and are limited to low representation expressiveness. The problem also gets progressively harder with the introduction of the target price sequence, which also contains stochastic noise and reduces generalizability at test-time. To tackle these issues, we combine a deep hierarchical variational-autoencoder (VAE) and diffusion probabilistic techniques to do seq2seq stock prediction through a stochastic generative process. The hierarchical VAE allows us to learn the complex and low-level latent variables for stock prediction, while the diffusion probabilistic model trains the predictor to handle stock price stochasticity by progressively adding random noise to the stock data. Our Diffusion-VAE (D-Va) model is shown to outperform state-of-the-art solutions in terms of its prediction accuracy and variance. More importantly, the multi-step outputs can also allow us to form a stock portfolio over the prediction length. We demonstrate the effectiveness of our model outputs in the portfolio investment task through the Sharpe ratio metric and highlight the importance of dealing with different types of prediction uncertainties. ...