Generating drawdown-realistic financial price paths using path signatures

ArXiv ID: 2309.04507 “View on arXiv”

Authors: Unknown

Abstract

A novel generative machine learning approach for the simulation of sequences of financial price data with drawdowns quantifiably close to empirical data is introduced. Applications such as pricing drawdown insurance options or developing portfolio drawdown control strategies call for a host of drawdown-realistic paths. Historical scenarios may be insufficient to effectively train and backtest the strategy, while standard parametric Monte Carlo does not adequately preserve drawdowns. We advocate a non-parametric Monte Carlo approach combining a variational autoencoder generative model with a drawdown reconstruction loss function. To overcome issues of numerical complexity and non-differentiability, we approximate drawdown as a linear function of the moments of the path, known in the literature as path signatures. We prove the required regularity of drawdown function and consistency of the approximation. Furthermore, we obtain close numerical approximations using linear regression for fractional Brownian and empirical data. We argue that linear combinations of the moments of a path yield a mathematically non-trivial smoothing of the drawdown function, which gives one leeway to simulate drawdown-realistic price paths by including drawdown evaluation metrics in the learning objective. We conclude with numerical experiments on mixed equity, bond, real estate and commodity portfolios and obtain a host of drawdown-realistic paths.

Keywords: generative modeling, drawdown simulation, variational autoencoder, path signatures, portfolio management

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts like path signatures, rough path theory, and non-linear dynamic systems to approximate drawdown, indicating high mathematical complexity. It includes numerical experiments on mixed asset portfolios and discusses model implementation, demonstrating substantial empirical work, though the excerpt focuses more on the theoretical framework than detailed backtesting results.

  flowchart TD
    A["Research Goal: Simulate Financial Price Paths<br>Realistic in Drawdown"] --> B["Methodology: Non-Parametric Monte Carlo"]
    B --> C["Generative Model: Variational Autoencoder"]
    B --> D["Core Innovation: Path Signatures"]
    C --> E["Input: Multi-Asset Historical Data<br>Equity, Bond, Real Estate, Commodity"]
    D --> E
    E --> F["Training: Learn Distribution with<br>Drawdown Reconstruction Loss"]
    F --> G["Output: Synthetic Price Paths"]
    G --> H["Findings: Drawdown-Realistic Paths<br>Quantifiably Close to Empirics"]