Non-Adversarial Calibration of Generative Market Models via Proper Scoring Rules

The paper trains neural-SDE market generators by minimizing a signature-kernel scoring rule — a strictly proper scoring rule on path space — instead of an adversarial GAN objective, yielding stable calibration of generative models for financial time series with a well-defined population minimizer. We read it as a principled replacement for fragile GAN training in market simulation.

The loss is a signature-kernel score (a kernel MMD) between generated and empirical path laws, S(P, Q) built from k_sig; the neural SDE dX = b_θ dt + σ_θ dW is fit by minimizing the expected score.

The substance is that a strictly proper scoring rule on paths removes the min–max instability of GANs while retaining a generator expressive enough for stylized facts. For risk work, a generator with a defined and consistent objective is auditable in a way an adversarial one is not.

Reinforces the desk preference for explicit, proper objectives over adversarial procedures when synthesizing scenarios; a scenario generator is only usable for risk if its training target is well-posed.

Signature-kernel scores are costly to evaluate and depend on kernel hyperparameters; fidelity to tail dependence still requires validation against held-out regimes.