Deep Generation of Financial Time Series

From GANs to Diffusion Models for Private Credit

A comprehensive PhD-level course on deep generative models for synthetic financial data generation, with focus on private credit applications and risk management.

View Slides Explore Literature
30
PhD-Level Slides
Beamer presentation with mathematical rigor
3,387
Papers Reviewed
Comprehensive OpenAlex literature search
24
Visualizations
Publication-quality charts and diagrams
1,050
Synthetic Data Points
1,000 loans + 50 funds simulated

Course Overview

Generative Adversarial Networks

  • GAN architecture and training dynamics
  • Mode collapse and solutions
  • WGAN with gradient penalty
  • TimeGAN for temporal data
  • Conditional GANs for regime-specific generation

Variational Autoencoders

  • Encoder-Decoder architecture
  • ELBO derivation and optimization
  • Reparameterization trick
  • Latent space visualization
  • Beta-VAE trade-offs

Diffusion Models

  • Forward and reverse diffusion processes
  • Score-based SDE formulation
  • GBM-Diffusion for finance
  • Price-proportional noise injection
  • Stylized facts reproduction

Private Credit Applications

  • Loan-level simulation (OU, CIR processes)
  • Fund-level NAV and J-curve modeling
  • Correlation structure and copulas
  • VaR and stress testing
  • Synthetic data for risk management

Mathematical Models Covered

GAN Objective

minG maxD E[log D(x)] + E[log(1-D(G(z)))]

VAE ELBO

L = Eq[log p(x|z)] - DKL(q(z|x)||p(z))

Diffusion Forward

q(xt|x0) = N(xt; sqrt(alpha)x0, (1-alpha)I)

Ornstein-Uhlenbeck

drt = theta(mu - rt)dt + sigma dWt

Cox-Ingersoll-Ross

d lambdat = kappa(theta - lambdat)dt + sigma sqrt(lambdat) dWt

WGAN Gradient Penalty

LGP = lambda E[(||grad D(x)||2 - 1)2]

Resources

📚

Presentation Slides

30 PhD-level Beamer slides with embedded visualizations
📖

Literature Review

Searchable database of 3,387 academic papers
📊

Chart Gallery

24 publication-quality visualizations
💾

Simulated Data

Synthetic private credit datasets

Key Research Topics

Generative Adversarial Networks Variational Autoencoders Diffusion Models Normalizing Flows Private Credit Time Series Generation Synthetic Data Risk Management Fat Tails Volatility Clustering Mode Collapse Score Matching VaR Estimation Stress Testing

Learning Objectives

1

Understand Stylized Facts

Master the statistical properties of financial time series including fat tails, volatility clustering, and leverage effects.

2

Master Generative Architectures

Learn GAN, VAE, and Diffusion model architectures with their mathematical foundations and training dynamics.

3

Apply to Private Credit

Generate synthetic private credit data at both loan and fund levels using stochastic processes.

4

Evaluate Synthetic Data

Apply FID, MMD, and ACF-based metrics to assess the quality of generated financial time series.

5

Implement Risk Applications

Use synthetic data for VaR estimation, stress testing, and scenario generation.