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I am investigating the suitability of using deep learning for pricing and calibration for the full implied volatility surface. Such examples of their application are in papers here and here. During examples, the latter achieved the calibration task in mere milliseconds, which were orders of magnitude faster than numerical approximations and monte carlo methods.

However, I was wondering what some of the drawbacks of using Deep Learning for this task could be, and whether there were any papers or research that highlight this issue. The latter paper cited 'cumbersome computations' during training, but I was wondering if there were any drawbacks regarding, perhaps, the architecture of DL networks as well?

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    $\begingroup$ Not sure if it is in scope of your question, but there was a recent article in Risk explaining some major banks have tried to implement deep learning techniques to automate hedging, and the performance seems to be extremely poor (~20%-30% lower PnL than using traditional hedging methods). $\endgroup$ Mar 22, 2021 at 18:53
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    $\begingroup$ Could you kindly providly a link to a paper or a source on this? Many thanks. $\endgroup$ Mar 23, 2021 at 11:35
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    $\begingroup$ "Deep hedging strays when volatility gets rough" - paywall though. $\endgroup$ Mar 23, 2021 at 12:44

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The essence of the problem is the "bias-variance" problem in machine learning. Which you can wiki (or find dozens of papers on; it's a famous issue).

You can, with ever greater complexity, create a model that ever-better explains history. But the "shortcuts" it uses to do this can sacrifice its ability to forecast new and unseen data. The model should be more uncertain and more prepared to allow historical mistakes to prevent overconfidence and reduce the chances of future ones.

It's the same problem, but just with newer tech, than the infamous "the backtests stop working once the structured product goes live" problem that has dogged finance for decades. The models are not "optimised"; they are "over-optimised" (for the past, and thus under-optimised for the future).

If shallow learning cannot solve the problem, it does not follow that the problem can be solved. Applying deeper and deeper and deeper learning until you can solve the bit of the problem you have in your sample is just ultra-sophisticated cheating. And the boss who pays your bonus doesn't understand the model anyway, so so long as the product is selling well, you both still get paid.

This, albeit put very bluntly, is a much bigger problem than arguing about the hyperparameters of this model or that. Both will torture the data to force it to "confess" that noise is signal if you want them to...

hope this helps, DEM

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Deep learning has drawbacks in that it can take a long time to train. In application, if the market conditions change, you can always use future market data that hasn't happened yet to feed in to your model to get an edge. Proven by the filtration $F_{t}$.

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  • $\begingroup$ What do you mean by 'take future values that hasn't happened yet'? This is impossible. $\endgroup$ Mar 22, 2021 at 18:42

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