Signatures for drawdown paths - A primer

A primer into using signature transform for modeling drawdowns

Published on November 01, 2021 by Emiel Lemahieu

Signature transform Drawdowns

1 min READ

My other projects hinge on the concepts of paths and path signatures as prerequisites. In the words of Terry Lyons1:

The key idea behind signatures is to stop thinking about a path as a quantity evolving over time, but rather as an object that you can query over intervals. As one queries these intervals, one gets a natural description about what happens with the system at different time scales.

The primer (based on Chevyrev et al. 2016) compiles my notes from a literature review on the signature transform, and includes two examples related to portfolio drawdown:

  • Classifying high- and low-drawdown stocks in terms of next period expectation using signature transformed previous period paths as features.
  • Distinguishing between high- and low-codrawdown regimes using signature embedded paths.
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Signatures for drawdown paths: A primer.

References

  1. Reference to this quote and highly recommended is this introduction to signatures and rough path theory given by Terry Lyons at the Royal Statistical Society in 2022 included above. ↩