Deep hedging strays when volatility gets rough – study

In the most realistic simulations, data-driven approach fared 30% worse than conventional hedging

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For derivatives hedgers preparing to throw out their Black-Scholes models in favour of new data-driven algorithms, a recent study may give pause for thought.

Banks such as JP Morgan have experimented in recent years with so-called deep hedging, in which machine learning systems are trained to hedge complex derivatives books. It’s an alternative to the use of conventional parametric models like Black-Scholes, which calculate options hedges based on variables such as the price of the underlying and its volatility.

The new study suggests the models could be sent off-course when markets exhibit memory effects. This behaviour is a known feature of markets, where the path of past events influences their future course.

But the kind of feed-forward neural networks widely used in finance take their cue from a snapshot of current data without asking how markets reached that point. As Blanka Horvath, an academic at King’s College London and one of the authors of the study, describes it, these feed-forward models effectively have no memory. 

The study’s simulations of hedging by the new models showed up “considerable errors”, Horvath says, when run with non-Markovian data – which is produced by models that exhibit such a memory effect. Losses for deep hedging in certain simulations were approaching 30% greater than when using a more conventional model.

To measure the effect of the models’ absence of memory, Horvath and her collaborators trained and tested a deep hedging model on synthetic data created using rough volatility modelling – a new approach shown to generate more lifelike data.

Rough volatility models explicitly capture the memory effect of markets, using a specific parameter. So the academics were able to run and compare multiple simulations, adjusting the parameter at each step to generate progressively more realistic datasets.

Being able to understand whether your machine learning model is giving you back your theoretical solution is immensely valuable

Blanka Horvath, King’s College London

“We were interested in understanding: if we blindly used deep hedging engines on data that does have these memory effects, how wrong could we get?” Horvath says.

Quite wrong, it turns out. The academics found the machine learning hedges to be worse than conventional hedging when applied to datasets in which the non-Markovian memory effect was present. And the distribution of returns in those simulations showed that deep hedging was liable to produce even greater losses in extreme market moves.

The results suggest that when markets exhibit extreme non-Markovian behaviour — something that may be more common during periods of stress — deep hedging may lose its way. Deep hedging registered a quadratic hedging loss of 0.67 in the worst case versus 0.52 for a simpler model hedge.

All of which points to the need for careful risk management of deep hedging models. “Naive application” of machine learning to real data could lead to “substantial errors”, the authors write.

Photo: Geraint Roberts

Blanka Horvath

Horvath says the study underscores the value of running machine learning and theoretical models side by side.

Quants can use rough volatility, she says, to cross-check the output from deep hedging models to ensure their black-box algorithms aren’t losing touch with the markets they track. When the deep hedging system diverged from the theoretical model, quants would know the algorithm needed retraining.

“Being able to understand whether your machine learning model is giving you back your theoretical solution is immensely valuable,” Horvath says. “It’s always good to have a model as backup to understand what can go wrong and how long it can go wrong for.”

Quants could also use rough volatility to solve another problem with deep hedging, she thinks – the synthetic data used for training can turn out to be a poor guide for the future. Deep hedging models demand more information to train on than history can provide. So, quants feed the systems with data from mathematical simulators.

Like the models themselves, though, synthetic data misses the autocorrelation effects and jumps seen in true markets. “If models are only trained on Markovian synthetic data, they will be unprepared for hedging scenarios where we need the memory effect,” Horvath explains. 

Hans Buehler, global head of equities analytics, automation and optimisation at JP Morgan and a high-profile exponent of deep hedging, agrees deep hedging systems trained with non-Markovian simulators should perform better in real markets that exhibit “rough” patterns.

The study shows, however, that deep hedging will struggle as much as theoretical models to hedge extreme risks in markets, says Artur Sepp, who heads research at quant hedge fund Quantica Capital.

Even when trained on fully non-Markovian data, the model came up with an imperfect hedge, he points out. “In reality, when you have these heavy-tailed distributions, as is the case in options markets, machine learning will not help you hedge losses arising from fat-tail events or from sudden jumps in price dynamics. Machine learning helps you to identify a good hedge, but it’s not perfect,” says Sepp.

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• Topics
• Black-Scholes
• Hedging
• Option pricing
• Volatility
• Risk management
• Cutting Edge
• Derivatives
• Machine learning
• Quantitative finance
• Deep hedging