Generating Financial Markets With Signatures

9 Pages Posted: 28 Aug 2020 Last revised: 1 Jun 2021

See all articles by Hans Buehler

Hans Buehler

JP Morgan

Blanka Horvath

ETH Zürich - Department of Mathematics

Terry Lyons

affiliation not provided to SSRN

Imanol Perez Arribas

University of Oxford - Mathematical Institute

Ben Wood

JP Morgan Chase

Date Written: July 21, 2020

Abstract

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.

Keywords: market generator, signatures, rough path theory, neural networks

Suggested Citation

Buehler, Hans and Horvath, Blanka and Lyons, Terry and Perez Arribas, Imanol and Wood, Ben, Generating Financial Markets With Signatures (July 21, 2020). Available at SSRN: https://ssrn.com/abstract=3657366 or http://dx.doi.org/10.2139/ssrn.3657366

Hans Buehler

JP Morgan ( email )

4/F, 25 Bank Street
London, E14 5JP
United Kingdom

Blanka Horvath

ETH Zürich - Department of Mathematics ( email )

R¨amistrasse 101
Raemistr. 101
Z¨urich, 8092
Switzerland

Terry Lyons

affiliation not provided to SSRN

Imanol Perez Arribas (Contact Author)

University of Oxford - Mathematical Institute ( email )

Andrew Wiles Building
Radcliffe Observatory Quarter (550)
Oxford, OX2 6GG
United Kingdom

Ben Wood

JP Morgan Chase ( email )

London
United Kingdom

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