Paper: arXiv 2604.07159

Authors: Alexandre Alouadi, Grégoire Loeper, Célian Marsala, Othmane Mazhar, Huyên Pham

Abstract

We study the problem of generating synthetic time series that reproduce both marginal distributions and temporal dynamics, a central challenge in financial machine learning. Existing approaches typically fail to jointly model drift and stochastic volatility, as diffusion-based methods fix the volatility while martingale transport models ignore drift. We introduce the Schrödinger-Bass Bridge for Time Series (SBBTS), a unified framework that extends the Schrödinger-Bass formulation to multi-step time series. The method constructs a diffusion process that jointly calibrates drift and volatility and admits a tractable decomposition into conditional transport problems, enabling efficient learning. Numerical experiments on the Heston model demonstrate that SBBTS accurately recovers stochastic volatility and correlation parameters that prior SchrödingerBridge methods fail to capture. Applied to S&P 500 data, SBBTS-generated synthetic time series consistently improve downstream forecasting performance when used for data augmentation, yielding higher classification accuracy and Sharpe ratio compared to real-data-only training. These results show that SBBTS provides a practical and effective framework for realistic time series generation and data augmentation in financial applications.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10 (capped from 7.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a mathematically sophisticated Schrödinger-Bass bridge framework to address drift and stochastic volatility simultaneously in synthetic financial data generation. It demonstrates strong empirical rigor through recovery of Heston parameters and practical utility via data augmentation on S&P 500 downstream forecasting.

Research Flowchart

  flowchart TD
    A[Goal: Generate synthetic financial time series capturing both drift & stochastic volatility] --> B[Input: S&P 500 Market Data & Heston Model Benchmark]
    B --> C[Framework: Schrödinger-Bass Bridge for Time Series SBBTS]
    C --> D[Method: Joint drift-volatility calibration via conditional transport decomposition]
    D --> E[Validation: Parameter recovery on Heston Model vs. prior SB methods]
    D --> F[Application: Financial data augmentation for downstream forecasting]
    E & F --> G[Outcomes: Accurately models stochastic volatility, improves forecasting accuracy & Sharpe ratios]

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3 of 87 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.