Abstract
We investigate the performance of the Deep Hedging framework under training paths beyond the (finite dimensional) Markovian setup. In particular, we analyse the hedging performance of the original architecture under rough volatility models in view of existing theoretical results for those. Furthermore, we suggest parsimonious but suitable network architectures capable of capturing the non-Markoviantity of time-series. We also analyse the hedging behaviour in these models in terms of Profit and Loss (P&L) distributions and draw comparisons to jump diffusion models if the rebalancing frequency is realistically small.
Highlights
Deep learning has undoubtedly had a major impact on financial modelling in the past years and has pushed the boundaries of the challenges that can be tackled: can existing problems be solved faster and more efficiently (Bayer et al 2019; Benth et al 2020; Cuchiero et al 2020; Gierjatowicz et al 2020; Hernandez 2016; Horvath et al 2021; Liu et al.2019; Ruf and Wang 2020), but deep learning allows us to derive solutions to optimisations problems (Buehler et al 2019), where classical solutions have so far been limited in scope and generality
In the current paper we go a step further than just presenting an ad hoc well-chosen market simulator: we investigate a situation where the relevant data are structurally so different from the original Markovian setup that it calls for an adjustment of the model architecture itself
Zhang 2019) and its performance against the deep hedging scheme in (Buehler et al 2019), which had to be adapted to a non-Markovian framework
Summary
Deep learning has undoubtedly had a major impact on financial modelling in the past years and has pushed the boundaries of the challenges that can be tackled: can existing problems be solved faster and more efficiently (Bayer et al 2019; Benth et al 2020; Cuchiero et al 2020; Gierjatowicz et al 2020; Hernandez 2016; Horvath et al 2021; Liu et al.2019; Ruf and Wang 2020), but deep learning allows us to derive (approximative) solutions to optimisations problems (Buehler et al 2019), where classical solutions have so far been limited in scope and generality These approaches are fundamentally data driven, which makes them attractive from business perspectives.
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