Quantum Finance: Practical Applications

Last time we talked about the Black-Scholes model. We dove into optimization about pricing options, but what about the average investor’s portfolio? What can quantum do to enhance the everyday investor? What are the practical applications of quantum finance?

Monte Carlo Derivative Pricing

Computational finance is vastly improved by the raw processing power improvement of quantum computing. With Google’s recent announcement of quantum supremacy, many speculators are researching a competitive edge for the derivatives market. Patrick Rebentrost published an outstanding paper on derivatives pricing in 2018 (source at the bottom). Below are a few insightful charts from the paper on the practical nature of quantum finance.

The distribution is log-normal in the Black-Scholes model. The squiggly lines represent 5 price evolutions (of a single security) plotted over time (days). As we saw last time with the Black-Scholes model, the key to pricing an option is the hedge optimization for volatility on the security over a time period. This chart shows us 5 possible outcomes. The two red dashed lines represent standard deviation, and the black dashed line represents mean. The average investor can use this chart to accurately predict when to buy or sell a derivative. The key quantum element here is the speed (raw processing power) at which these predictions can be made, as well as the optimization for volatility.

The next chart demonstrates the "scaling of error" in classical and quantum Monte Carlo methods. The quantum error (quadratic) is bounded by the green line. The error correction and computation required for classical MC methods is far greater than quantum MC methods. Banking Another interesting area of quantum finance would be banking and risk assessment. Imagine an algorithm that can instantaneously determine a borrower's validity for a loan. While there are great classical computational algorithms that exist already (with hundreds of variables), quantum computers could effectively teach out-dated banking systems a borrower's entire financial history, income, potential income, and more. However, this does pose quite the risk in terms of cyber security. The quantum algorithm could effectively extract vital information from public data, and create a personal profile for every person who's ever opened a bank account. This would have dire consequences for the average borrower's socioeconomic future. What is Quantum Thought up to? There are tons of other areas in finance quantum computing can optimize such as: financial modeling (3D) and forecasting, financial system restructuring, high frequency trading, as well as corporate accounting. Quantum Thought is currently exploring: optimizing portfolio algorithms, financial instrumentation, and more.

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.022321