A diffusion model trained with Gauss-Hermite quadrature generates synthetic equity returns that pass a univariate Cramér-von Mises test on an equally weighted portfolio and yield better-conditioned covariance matrices than the historical sample.
W.: On the distribution of the two-sample Cramer-von Mises criterion,The Annals of Mathematical Statistics, 1148 - 1159 (1962)
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Beyond Monte Carlo: Harnessing Diffusion Models to Simulate Financial Market Dynamics
A diffusion model trained with Gauss-Hermite quadrature generates synthetic equity returns that pass a univariate Cramér-von Mises test on an equally weighted portfolio and yield better-conditioned covariance matrices than the historical sample.