A Data-driven Market Simulator for Small Data Environments

Abstract

Neural network based data-driven market simulation unveils a new and flexible way of modelling financial time series, without imposing assumptions on the underlying stochastic dynamics. Though in this sense generative market simulation is model-free, the concrete modelling choices are nevertheless decisive for the features of the simulated paths. We give a brief overview of currently used generative modelling approaches and performance evaluation metrics for financial time series, and address some of the challenges to achieve good results in the latter. We also 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 notoriously small. Furthermore, we show how a rough paths perspective combined with a parsimonious Variational Autoencoder framework provides a powerful way for encoding and evaluating financial time series in such environments where available training data is scarce. Finally, we also propose a suitable performance evaluation metric for financial time series and discuss some connections of our Market Generator to deep hedging.

Discriminating modelling approaches for Point in Time Economic Scenario Generation

“…In order to achieve this, raw financial data needs to undergo transformations to be modelled without the hindrances of stylized facts and model assumptions need to be examined in order to justify their usage. Possible transformations include those described as quest for invariants in [23] or the reformulation into their signatures as proposed in [18].…”

“…Classically, comparison between the similarity of distributional properties relies on statistical measures such as QQ Plots, Tail Behaviour measures, correlation measures etc as used in [11] or [30]. These approaches however might face a variety of problems as described in [18], given by different usages of the scenario generation (see examples from introduction), be it optimization with respect to certain options or a portfolio performance. Other difficulties in performance evaluation arise for example also due to the non continuity of the given data or the intractability of the true underlying distribution.…”

“…Other difficulties in performance evaluation arise for example also due to the non continuity of the given data or the intractability of the true underlying distribution. Approaches to counter these problems could be the usage of signature transforms and Maximum Mean Discrepancy as performance measure as given in [18].…”

“…As parametric model we assume a GARCH process ( [14]) with a joint likelihood estimation using an autoregressive model for the VIX as used in [15], and we choose generative neural networks as data driven models, known in scenario generation as Market Generators following the notation in [11]. More specifically, we extend the research of [11] on using Bernoulli Restricted Boltzmann machines ( [16]) as market generators with a conditioning factor and additionally include in the comparison a conditional Variational Autoencoder ( [17]), where we use labels for the forward looking VIX information similar to [18].…”

Risk-Neutral Market Simulation

“…To address this data scarcity challenge, there has been much work in the area of using generative machine learning models to simulate realistic samples from the same distribution as the historical market data. To name a few: (Arribas, Salvi, and Szpruch 2020;Buehler et al 2020;Wang 2021, 2022;Cuchiero, Khosrawi, and Teichmann 2020;De Meer Pardo, Schwendner, and Wunsch 2021;Gierjatowicz et al 2020;Ni et al 2020Ni et al , 2021Wiese et al 2019Wiese et al , 2020.…”