Ambiguity-Averse Deep Hedging of Options under Controlled Distributional Shifts

Standard deep hedging optimises a risk criterion under a single reference probability measure. Ambiguity-averse extensions try to account for model uncertainty by clustering training paths into market regimes and hedging against the worst of them. But how well this works should depend on the distance between the training distribution and the distribution the hedger is actually tested on. However, that distance is generally not explicit. We build a simple, controllable way to measure it: a family of mixtures between a Heston and a GARCH generator, parametrised by a single mixture weight, that interpolates continuously between a baseline training regime and a more realistic one. This lets us move the test distribution away from the training distribution by a known amount and watch what happens. Across this whole range, and on ten years of real index data, the standard deep hedger consistently beats the ambiguity-averse one on both risk and variance, though the ambiguity-averse hedger is reliably cheaper for what concerns transaction costs. This is different from what the paper we build on reports. Tracing the discrepancy, in direct correspondence with its authors, led to a sign error in their volatility model's correlation parameter, which quietly changes what kind of market stress the hedger is trained to survive. We discuss what this means, how the original results should be read, and end with some preliminary findings, left for future work.