Hedging is, of course, a ubiquitous practice in FS and there are well-developed classical computational approaches for implementing this risk mitigation strategy. The challenge has been the computational cost and time-to-solution for more complex hedges and longer timeframes. Today, JPMorgan Chase and quantum algorithm specialist QC Ware issued a paper (Quantum Deep Hedging) that breaks new ground in using Deep Hedging on a quantum computer.

“We prove that the quantum neural networks we use are trainable, and we perform extensive simulations that show that quantum models can reduce the number of trainable parameters while achieving comparable performance and that the distributional approach obtains better performance than other standard approaches, both classical and quantum,” write the researchers[i].

The work was done on Quantinuum H1-1 and H1-2 trapped-ion QPUs and used circuits with up to 16 qubits. The team performed inference using two sets of Quantum Deep Hedging models which were classically pre-trained. “First, we used the policy-search based algorithm with the LSTM and Transformer architectures instantiated with 16-qubit orthogonal layers. Second, we used the novel distributional actor-critic algorithm instantiated with compound neural networks using up to 12 qubits. We observed close alignment between noiseless simulation and hardware experiments, with our distributional actor-critic models again providing best performance,” according to the paper.

It’s thought the financial services sector will be an early adopter of quantum computing because it has both the need and resources. Here is a little more background (lightly edited) on the hedging use case as described in the paper:

“Classical financial mathematics provides optimal hedging strategies for derivatives in idealized friction-less markets, but for real markets these strategies must be adapted to take into account transaction costs, market impact, limited liquidity, and other constraints. Deep Hedging is a framework for the application of modern reinforcement learning techniques to solve this problem.

“One starts by defining a reinforcement learning environment for the hedging problem and a trading goal of maximizing a risk-adjusted measure of cumulative future returns. Then, one can apply standard deep reinforcement learning algorithms, such as policy-search or actor-critic approaches, by designing neural network architectures to model the trading strategy and by defining a training loss function to find the optimal parameters that maximize the trading goal.

“Beyond Deep Hedging, the applicability of machine learning to finance has grown significantly in recent years as highly efficient machine learning algorithms have evolved over time to support different data types and scale to larger data sets. For instance, supervised learning can be used for asset pricing or portfolio optimization, unsupervised learning for portfolio risk analysis and stock selection, and reinforcement learning for algorithmic trading.”

This work looked at quantum networks with orthogonal and with compound layers. The is paper is best read directly. The researchers say, “We believe our quantum reinforcement learning methods have applications beyond Deep Hedging, for example for algorithmic trading or option pricing, and it would be interesting to develop specific quantum methods for such problems. Note that in these use cases the training data can be produced efficiently, removing the bottleneck of loading large amounts of data onto the quantum computer.”

That said, the authors acknowledge open questions remain.

Iordanis Kerenidis, head of quantum algorithms at QC Ware, is quoted in press release, “The results achieved with JPMorgan Chase demonstrate the huge potential and applicability of quantum machine learning, both today, by using quantum ideas to provide novel models with classical hardware, and also leveraging the continuously more powerful quantum hardware we anticipate in the future.”

Marco Pistoia, managing director, head of Global Technology Applied Research, JPMorgan Chase, noted. “As quantum computing continues to mature, JPMorgan Chase’s leading position will only be further solidified via future-ready algorithms that will produce continually improving results.” (See earlier HPCwire article, JPMorgan Chase Bets Big on Quantum Computing)

Link to paper, https://arxiv.org/pdf/2303.16585.pdf

[i] El Amine Cherrat1,2*, Snehal Raj1, Iordanis Kerenidis1,2, Abhishek Shekhar3, Ben Wood3, Jon Dee3, Shouvanik Chakrabarti4, Richard Chen4, Dylan Herman4, Shaohan Hu4, Pierre Minssen4, Ruslan Shaydulin4, Yue Sun4*, Romina Yalovetzky4, Marco Pistoia4

1QC Ware
2Université de Paris, CNRS, IRIF 3Quantitative Research, JPMorgan Chase 4Global Technology Applied Research, JPMorgan Chase