Generating Financial Markets With Signatures

Neural network based data-driven market simulation unveils a new and flexible way of modelling financial time series, which has recently inspired a surge of research activity in the quantitative finance community. Though generative market simulation is model-free in the sense that it makes no assumptions on the stochastic dynamics of the underlying paths, the concrete modelling choices are nevertheless decisive for the performance of the resulting market generators and the features of the simulated paths. We contrast some classical approaches of market simulation with simulation based on generative modelling and highlight some advantages and pitfalls of the new approach. While most generative models tend to rely on large amounts of training data, we present here a generative model that works reliably even in environments where the amount of available training data is small, irregularly paced or oscillatory. We show how a rough paths-based feature map encoded by the signature of the path outperforms returns based market generation both numerically and from a theoretical point of view. Finally, we also propose a suitable performance evaluation metric for financial time series and discuss some connections of our signature-based Market Generator to deep hedging.