Present-day quantum computers are middle-to-late stage prototypes equipped with a limited number of noisy qubits that produce many errors and operate with low fidelity. By contrast, truly useful finance applications all have complex computations that need huge numbers of high-fidelity qubits and some form of practical error correction in order to run them. So even though significant progress has been made on error correction and error mitigation, fault-tolerant quantum computers are still several years away.
However, based on technology roadmaps that have been recently published within the quantum ecosystem, it appears that quantum computers will likely exceed the computational power of classical computers sometime in the latter part of this decade. Once this milestone is achieved, quantum computing will be transformative for many industry sectors. And, given the amount of quantum research that has been conducted across a wide spectrum of financial use cases, I believe that finance will be one of the first sectors to showcase quantum advantage.
In the long run, experts believe that quantum computers will be able to outperform classical computers and solve complex financial applications such as portfolio optimization, risk analysis and option pricing by using the quantum mechanical principals of superposition and entanglement.
Early deep hedging algorithms
JPMorgan Chase has a long history of continually advancing its trading technology. In 2018, a team of diverse researchers, Hans Buehler, Lukas Gonon, Josef Teichmann, and Ben Wood (JCMorgan Chase), developed a stochastic model on Deep Hedging. Later in 2019, JPMorgan Chase finance researchers improved on that research by developing a realistic equity option market simulator based on generative adversarial networks (GANs).
In financial markets, hedging is a trading strategy designed to minimize risk. Buyers and sellers of derivative contracts sometimes also trade the underlying assets associated with the derivative as a cushion against unfavorable price fluctuations. Besides its direct application to hedging, the JPMorgan Chase researchers’ breakthrough was the first successful demonstration of generative adversarial networks (GANs) used to create a multivariate financial time series for simulating the option market.
Today’s prototype quantum computers aren’t powerful enough to run large and useful financial applications like this. However, despite technical limitations, today’s quantum machines don’t restrict the development and testing of quantum algorithms. Generally, algorithms can be created that are far more advanced than the quantum hardware that would be required to run them. Successful algorithms that demonstrate potential after testing can be saved for later use when larger-qubit models or even fault-tolerant quantum machines become available. This is a common “get ready for quantum” strategy employed by large compute-intensive companies.
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One of the problems with traditional mathematical hedging models, such as the 2019 model mentioned above, is that they employ only limited representations of actual market conditions. In real markets there are a number of conditions that should be taken into account for developing hedging strategies. These include such things as transaction costs, market impact, limited liquidity and others.
Retooling a deep hedging algorithm
Earlier this year, JPMorgan Chase, QC Ware and the University of Paris successfully developed and used deep reinforcement learning algorithms and quantum computing to improve on the 2019 deep hedging model. The team also designed two additional and important algorithms that contributed to the success of the project: a policy search algorithm and an actor-critic algorithm. These are explained later in this piece.
This project was the first collaboration between JPMorgan Chase and QC Ware. I had the opportunity to discuss the new deep hedging algorithm and how it was developed with two key members of the research team:
- Dr. Marco Pistoia is managing director, distinguished engineer, head of global technology applied research and head of quantum computing at JPMorgan Chase & Co.
- Dr. Iordanis Kerenidis is the senior vice president of quantum algorithms at QC Ware Corp. research director at the Centre national de la recherche scientifique (CNRS) and director at the Paris Centre for Quantum Computing
According to Dr. Pistoia, JPMorgan Chase has done a lot of prior work on algorithms for derivative pricing and hedge derivatives. However, this is the first time that the deep hedging problem has been approached from a quantum perspective.
“We are very happy with the results,” Dr. Pistoia said. “Of course, we cannot use this algorithm in today’s production environment because the hardware is not yet up to speed. However, the essence of our work is to become quantum ready. So we build the algorithms and then when the hardware catches up, we have the algorithms ready. And, we’re also happy because in this case we have a higher-quality solution.”
Difference between classical and quantum deep hedging
Let’s take a high-level look at how the quantum deep hedging algorithm works by starting with a futures asset on a routine trading day. Once a price for the asset comes in from the market, we need to decide on a strategy to determine how much of this asset we should buy or sell. We know that the asset matures at some point, perhaps at the end of the month or the end of the year, so we need a hedging strategy to protect our investment until maturity.
The ultimate goal is to determine what the return would be when the asset matures, a factor that depends on future price changes. But of course, we don’t know what will happen in the future because there are an exponential number of different possible futures.
Therein lies the problem with the classical hedging model. Because it is classical it is only capable of looking at a relatively small number of possible futures before it computes an average to obtain the most probable value.
The quantum hedging model is much more sophisticated. Rather than being limited to just a few glimpses of the future, quantum superposition allows it to extract important information about all possible futures, such as what the overall distribution of returns looks like, what the most probable future is, what its skewness is and what shape the distribution has.
Because the model’s objective is to minimize risk, it is important for it to have access to the most-probable futures as well as futures with only a small probability. Whatever the actual future turns out to be will determine whether the model’s valuation of the asset results in a profit or a loss.
The model’s quantum neural network is used to load the superposition of all possible futures. Then those values are used to train the model. Obviously, having the superposition of all futures provides much better information about potential returns and allows a better trading strategy to be developed.
As mentioned earlier, the policy search algorithm and the actor-critic algorithm provide learning and optimization mechanisms that enable quantum deep hedging to adapt to changing market conditions and optimize trading strategies:
- The policy-search algorithm uses a neural network to model the trading strategy by repeatedly evaluating the policy’s decision-making rules, then updating the neural network’s parameters accordingly.
- The distributional actor-critic algorithm uses two elements, actor and critic, to determine the best trading strategy. The actor represents the trading strategy and decides what action to take—either buy, sell or hold—for any given market condition. The critic evaluates the actor’s decisions by estimating the distribution of potential returns, while also considering the risk and uncertainty of the transaction.
Dr. Pistoia said, “This is the first time that the distributional version of the actor-critic [algorithm] has been used for hedging. It is also the first time that we used distributional reinforcement learning, which is a relatively new technique that was developed by the Google DeepMind team a few years ago.”
Google acquired DeepMind in 2014. In 2020, researchers used distributional reinforcement learning to train digital agents to play Atari games better than humans. DeepMind researchers collected data from expert human players, then used that information to train a deep neural network to predict the distribution of rewards for each state-action pair. As an example, an agent might have an 80% chance of receiving a 25-point reward for taking an action in a certain game state, and a 20% chance of receiving no reward. Agents were able to use this information to make decisions about which actions could maximize the expected reward.
It is easy to see how this could be applied to the agent-critic algorithm in deep hedging. It is a promising new approach to reinforcement learning that can be used to solve a wide range of problems.
Dr. Kerenidis put the technique in perspective. “What we found out from this research is that quantum is actually natively very good in a distributional approach because quantum states can naturally hold large distributions,” he said. “This was the right framework to use, and because it’s so natively quantum, quantum reinforcement learning, and in particular the distributional actor-critic algorithm, is very effective and produces very good results.”
I asked Dr. Kerenidis how the algorithm handled incoming sequential pricing data. “We had to design new types of quantum neural networks to deal with time series and sequential pricing data,” he explained. “We also had to develop a quantum framework for distributional reinforcement learning. This is also a very new technique on the classical side, but we were able to bring these two things together to get quantum deep hedging.”
Choice of quantum computers
This research was done on Quantinuum’s H1-1 and H1-2 trapped-ion quantum processors, utilizing circuits with up to 16 qubits. (Quantinuum’s model H2 wasn’t available until after this research was published.) The observed performance agrees well with noiseless simulation. In this context, a noiseless simulation is a research tool that allows developers to simulate a perfect quantum computer to gauge how an algorithm would perform without the presence of noise or errors. The researchers believe their quantum techniques can be used for other reinforcement learning problems beyond hedging.
“Quantinuum’s quantum computer has the highest quantum volume in the market,” Dr. Pistoia said. “So some of these problems benefit from long coherent times, allowing us to run deeper circuits before qubits start to decohere.
“We were able to see very good results using real quantum hardware,” Dr. Pistoia added. “This is actually important because we cannot run these experiments in production, but getting expected results on a smaller scale gives us confidence that quantum computing is on the right track to become a production technology and also that our algorithm is correct.”
The Black-Scholes model was introduced in 1973. Prior to its development, there were no standard methods available to price option contracts or to evaluate option risk. Despite its limited constraints and its assumptions about constant volatility and returns that follow a normal distribution, the model is still an important tool in finance.
In this instance, the quantum hedging researchers used Black-Scholes as a baseline model for comparison. Since the assumptions of Black-Scholes sometimes differ from actual market conditions, Dr. Kerenidis said the team added frictions in the market such as transaction costs. “When we say that we have good results, that means we can do more than 10% better than Black-Scholes,” he said. “We found that our quantum methods can improve over Black-Scholes’ basic strategy.”
Development of this quantum deep hedging algorithm is important research for several reasons:
A. The researchers replaced a classical bottleneck in the original 2019 algorithm with a quantum solution but left the basic logic of the original algorithm intact.
B. This research represents a turning point because the algorithm demonstrates quantum computing’s deep learning capabilities, not only in finance, but in the general area of machine learning.
C. The researchers cleverly used superposition to analyze all possible future values simultaneously. This cannot be done classically because the problem is exponentially complex. An attempt to solve it classically would limit the solution to suboptimal approximations.
D. Overall, the research team met these objectives for developing the quantum deep hedging model:
- Quantum neural networks were proven to be trainable.
- Extensive simulations demonstrated quantum models can reduce the number of trainable parameters while also achieving comparable performance.
- The distributional approach produced better performance than standard classical and other quantum approaches.
Dr. Pistoia wrapped up our discussion with this comment: “For now we’re very happy with the results. One thing I want to emphasize is that JP Morgan Chase is not just a bank. As you can see, we are a technology company as well. We have a research lab, and we publish all of our research. For now, this collaborative research team would like to get feedback from the scientific community on our quantum approach to deep hedging. There may be a few more versions of this work in the future if we determine there are new improvements possible.”