3 research outputs found
Random neural networks for rough volatility
We construct a deep learning-based numerical algorithm to solve
path-dependent partial differential equations arising in the context of rough
volatility. Our approach is based on interpreting the PDE as a solution to an
SPDE, building upon recent insights by Bayer, Qiu and Yao, and on constructing
a neural network of reservoir type as originally developed by Gonon,
Grigoryeva, Ortega. The reservoir approach allows us to formulate the
optimisation problem as a simple least-square regression for which we prove
theoretical convergence properties.Comment: 33 pages, 3 figure
Deep Hedging under Rough Volatility
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 with view to existing theoretical results for those. Furthermore, we
suggest parsimonious but suitable network architectures capable of capturing
the non-Markoviantity of time-series. Secondly, we analyse the hedging
behaviour in these models in terms of P\&L distributions and draw comparisons
to jump diffusion models if the the rebalancing frequency is realistically
small