Equity Market Regime Detection Using the Euler Characteristic Curve of the Options Surface

Commonly used regime indicators (e.x. VIX) reduce the options market to a single number. I question if the surface contains complexities relevant to regimes that are abstracted by scalar quantities reducing the surface to a singular number. This paper explores regime detection by topologically analyzing the SPY options surface by, with respect to the DTE and Strike Price axes, partitioning a surface into nine equal zones, computing an Euler Characteristic Curve (ECC) on said zones, and concatenating curves in such a way to where it is 1-dimensionally represented, rendering it able to be used as input to a random forest. I evaluate its relative efficacy by comparing the ECC’s classification performance and the timing of its regime flags to random forests trained on traditional scalar quantities. On a 2021–2023 held-out test set, the ECC reaches ROC-AUC 0.80 (MCC 0.51), compared with at most 0.67 for VIX, SMA200, momentum, and conventional-indicator baselines, although a normalized scalar-shape summary matches or exceeds it on MCC and balanced accuracy. The ECC flagged both "true" regime transitions in the test window before their retrospectively dated turning points in a timing analysis. The results are limited by a lack of sufficient regime episodes needed to make a generalization as well as an algorithmic labeling error that affects part of the test window; this study is meant to provide a basis for further exploration rather than establish a new method.