Conditional Neural SDEs for Financial Time-Series Generation

Sina Molavipour; Alireza M. Javid; Björn Löfdahl; Mikhail Nechaev

stat.MLOct 30, 2026

Conditional Neural SDEs for Financial Time-Series Generation

Authors: Sina Molavipour, Alireza M. Javid, Björn Löfdahl, Mikhail Nechaev

Abstract

Conditional generation of time-series paths is a central problem in probabilistic modeling, where the goal is to simulate future trajectories that are both realistic and responsive to external context. It has direct applications in finance and economics. Neural stochastic differential equations provide a natural framework for this task by combining continuous-time stochastic dynamics with learnable drift and diffusion functions. However, directly modeling the target state can be unstable in conditional settings, especially when the target and conditioning variables have strong level dependence, limited training data, or different dimensions.We propose a residualanchor Neural SDE architecture that decomposes the target into a learned conditional anchor and a stochastic residual. The anchor captures the context-dependent baseline, while the Neural SDE (Stochastic Differential Equation) models the residual dynamics around this baseline. This separation reduces the burden on the stochastic dynamics and generalizes spread-based representations to more general conditioning settings.We evaluate the approach on real-world financial time series, including conditional interest-rate scenarios and a comparison with a time-series foundation model. The results show that the proposed model can generate plausible conditional paths, maintain competitive point accuracy, and provide calibrated uncertainty estimates.

Figures & tables

Figure 1. Estimated drift function $f_{\theta}(X)$ , and numerical estimation of the OU model for synthetic Vasicek time-series, with respect to state $X$ .

Figure 2. Backtesting conditional CIBOR scenarios generated by the residual-anchor Neural SDE. The model simulates $100$ -day paths for CIBOR (1Y), (5Y), and (8Y), conditional on the realized EURIBOR (1Y).

Figure 3. Monthly rolling backtest of the residual-anchor Neural SDE for CIBOR (1Y) conditioned on EURIBOR (1Y) over 2023–2026.

Figure 4. Conditional STIBOR (1Y) scenario generation using EURIBOR (1Y) as the conditioning signal.

Figure 5. Conditional STIBOR (1Y) scenario generation using both EURIBOR (1Y) and EUR/SEK as conditioning signals.

Figure 6. Comparison between our proposed Neural SDE and the BISTRO foundation model for US CPI YoY inflation scenarios conditional on the oil price path.

Figure 7. Historical backtest comparison between the residual-anchor Neural SDE and BISTRO for US CPI YoY inflation conditioned on oil prices. Metrics report point accuracy, coverage, and interval width.

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Francesco Piatti, Andrea Iannucci, Thomas Cass

Department of Mathematics, Imperial College London

Stochastic Differential Equations

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Feb 23, 2026

Generative Modeling via Kernelized Stochastic Interpolants

We develop a kernel method for generative modeling within the stochastic interpolant framework, replacing neural network training with linear systems. The drift of the generative SDE is

\hat b_t(x) = \nablaφ(x)^\topη_t

, where

η_t \in \mathbb{R}^P

solves a

P\times P

system computable from data, with

P

independent of the data dimension

d

. Since estimates are inexact, the diffusion coefficient

D_t

affects sample quality; the optimal

D_t^*

from Girsanov diverges at

t=0

, but this poses no difficulty and we develop an integrator that handles it seamlessly. The framework accommodates diverse feature maps: scattering transforms, pretrained generative models, etc, enabling generation and model combination without neural network training. We demonstrate the approach on financial time series, turbulence, and image generation.

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Stochastic Differential Equations Stochastic Interpolants Generative Modeling Kernel Methods

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Murex SAS · École Polytechnique · BNP-PAR and Ecole Polytechnique

Financial Time Series Stochastic Optimal Control Stochastic Differential Equations

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Abstract

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