Branched Signature Model: Universal Approximation and Efficient Computational Framework
ORIGINAL / Branched Signature Model
This paper introduces the branched signature model, generalizing classical geometric rough paths based on branched rough path theory, and establishes a universal approximation theorem. By constructing an extension map, branched signatures are realized as classical geometric signatures of extended paths, providing a computational scheme for data-driven modeling such as rough volatility calibration and optimal execution.
01 ABSTRACT
The authors introduce the branched signature model, extending the classical geometric rough path framework, and establish a universal approximation theorem. They also show that iterative compositions of lower-level signature maps can approximate higher-level signatures, and explicitly construct path extensions based on an existing extension map so that branched signatures can be realized as classical geometric signatures. Two applications—rough volatility calibration and optimal execution—demonstrate the framework's effectiveness, though the abstract does not report quantitative comparisons.
02 KEY FINDINGS
- Proposes the branched signature model, generalizing classical geometric rough paths, and establishes a universal approximation theorem.
- Shows that iterative compositions of lower-level signature maps can approximate higher-level signatures, providing a computational scheme.
- Constructs explicit path extensions using an existing extension map to realize branched signatures as classical geometric signatures.
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