For the past 60 years, digital computers (DCs) have become indispensable tools of modern society. Algorithms are so pervasive that we use them every day barely noticing. Algorithms perform most of commercial flights’ operations, choose our commuting route for avoiding traffic, find the websites that match a searched term… Our smartphones are more powerful than the systems used by NASA to put a man on the moon. Why would we need a new computing paradigm, when the current one seems to satisfy our every need?
No matter how fast and powerful DCs may become, some problems are simply intractable. Finance has a good lot of them. A few examples:
- Dynamic portfolio optimization: Computing an optimal trajectory for a portfolio under realistic assumptions is a NP-Complete problem. See an example here: http://ssrn.com/abstract=2649376
- Clustering: Clustering algorithms often rely on heuristics. It would be desirable to replace some of these heuristics with a brute force search over an unfathomably large number of combinations. Good clustering methods have applications on risk management and regression analysis. See an example here: http://ssrn.com/abstract=2708678
- Scenario analysis: Often investors would like to evaluate the distribution of outcomes under an extremely large number of scenarios, generated at random. Current approaches, like copulas, are too unrealistic/restrictive.
- Option pricing: Some complex derivatives are path-dependent. Evaluating a large number of paths can be computationally expensive.
There is no hope for solving these problems in polynomial time, much less ever finding a closed-form analytical solution. Quantum Computing (QC) offers the promise of being able to solve these problems in a matter of days, rather than in years.
Suppose that you are a large asset manager. Every time you rebalance your portfolio, your investors lose a fortune, as a consequence of transaction costs and price impact (slippage). In an environment where most funds struggle to make single digit returns, losing 3% on rebalancing costs is a death sentence by a thousand cuts. A QC could find a portfolio that is globally optimal over multiple investment horizons, hence significantly reducing the need for rebalances and their associated losses. QCs’ advantage is not that they can compute such portfolio faster than DCs. DCs simply cannot solve this problem for us. A second advantage is, by reducing the need for rebalancing, large asset managers will starve the high frequency algorithms that prey on them. So rather than trying to legislate against high frequency algorithms (a task that, 6 years after the flash crash, has led to nothing), maybe we should just let them go bankrupt.
This is merely one example of how QCs could solve several major challenges faced by finance professionals. In a few years, QC applications will disrupt finance just as much as the DCs transformed our business decades ago. And like with every disruptions, there will be winners and losers. It is important for professionals to become acquainted with some basic features of QCs, so that they don’t get left behind.
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