Time-Causal VAE: Robust Financial Time Series Generator

For financial time series, the shortage of samples makes it statistically hard for empirical processes to achieve an acceptable confidence level in describing the underlying market distribution. In practice, it is widely recognized among financial engineers that back-testing exclusively on empirical market data results in significant over-fitting, which leads to unpredictably high risks in decision making based on these tests [Bai+16]. Synthetic data are therefore generated to augment scarce market data, and used to improve backtesting, stress-testing, exploring new scenarios, and in deep learning processes in financial applications; see the overview given in [Ass+20a]. For those purposes, the generated data should look like plausible samples from the underlying market distribution, for example reproducing stylized facts observed in the market. In particular, we want the distribution of the generated data to be close to the underlying market distribution in their performance on decision making problems, such as pricing and hedging, as well as optimal stopping and utility maximization. Notably, these problems are not continuous with respect to widely used distances, such as the Maximum Mean Discrepancy (MMD) and the Wasserstein distances (W-distances). On the other hand, these problems are Lipschitz-continuous with respect to stronger metrics, called adapted Wasserstein distances (AW-distances) [Bac+20; PP14].