Quantum Computing Meets Finance

As an undergraduate economics major, I liked the courses in math, statistics, and economic and political history. One course in time series stood out. From then on, I fell in love with time-series econometrics.

It’s applying time-series methods—statistical techniques for analyzing data collected over time—to solve real-world economic modeling and/or prediction problems.

Today, we’re in an era of big data. But when I started my career, financial time series—and in particular asset prices—were among the largest datasets available for finance and economics research. We used models derived from theoretical developments to price financial derivatives, among other things.

In many sciences, you have data sampled at different time frequencies. In economics, the example that’s often quoted is “nowcasting.” Say it’s mid-August, and you want to predict the GDP at the end of 3rd and 4th quarters. But how do you predict low-frequency series like GDP growth from high-dimensional high-frequency data collected monthly, weekly, or even multiple times a day?

Working with several collaborators, I developed econometric methods known collectively as mixed-data sampling, or MIDAS, for combining data at different frequencies. It is regression based, so we’re talking about machine learning. But we’re still taking baby steps of doing machine learning with quantum computers.

Many financial-asset-pricing problems boil down to solving integral or partial differential equations. Quantum linear algebra can potentially speed that up. But the solution is a quantum state. So, you need to be creative about capturing salient properties of the numerical solution to your asset-pricing model. Additionally, pricing models are subject to ambiguity regarding sources of risk—factors that can adversely affect an asset’s value. Quantum information theory provides tools for embedding notions of ambiguity.

Recall that some of the pioneering research on quantum algorithms was done in the 1990s by scientists like Deutsch, Shor, and Vazirani, among others. Today it’s still a challenge to implement their ideas with current hardware, and that’s three decades later. But besides hardware, we need progress on algorithms—there’s been a bit of a quantum algorithm winter.

Optimization tasks across industries, including computational chemistry, materials science, and artificial intelligence, are also applied in the financial sector. These optimization algorithms are making progress. In particular, the ones related to quantum annealing are the most reliable scaled hardware out there (see Synopsis: Quantum Annealers Limited by Temperature). The downside is that you need a finance problem that fits. If you must torture yourself to make it fit, it’s not ideal.

The most well-known case is portfolio allocation. You have to translate that into what’s known as quadratic unconstrained binary optimization, which means making compromises to maintain what you can actually compute. Quantum annealing algorithms can solve combinatorial optimization problems like this more efficiently by exploring large solution spaces in parallel.

Another less well-known example is simulating asset-price dynamics. The financial mathematics is based on continuous-time stochastic differential equations. Realistic models feature time-varying volatility, which is a key property of asset-price movements. But you can’t implement stochastic volatility diffusion models on a quantum computer. Instead, you can implement a discretization of the continuous problem—increments of a week, say—but that ends up being very coarse and requires a rethinking of the asset-pricing dynamics.

You have to rewrite models in terms of a family that is amenable to quantum hardware. That includes hidden-Markov-chain models, which can capture complex dynamic patterns. Some of my research has focused on such processes for the purpose of pricing and shown the potential of quadratic speedups in credit risk and derivative-pricing computations.

A recent report by McKinsey & Company suggested that quantum computing use cases in the financial services industry could generate up to $622 billion in value by 2035. And in August the Financial Times reported that IBM and Google are still publicly aiming for industrial-scale quantum computers before 2030. The optimism is revealing.

I do think we’re revisiting a scenario that we’ve seen before. In the 1970s and 1980s, option pricing formulas were discovered in mathematical finance. There was a rush on Wall Street to hire people who could solve partial differential equations, among them physics degree holders. But the most successful people were those who had knowledge about physics but also understood the financial sector. Perhaps financial-engineering programs will start teaching nuts and bolts of finance, as well as the nuts and bolts of quantum. That’s what I expect to happen by analogy.