# How to apply quantum physics to trading

Stock market forces can be modeled with a quantum harmonic oscillator by Lisa ZygaPhys.

One example of this is illustrated in a new study, in which researchers show that the restoring force in a vibrating quantum harmonic oscillator provides a good approximation of the market force that restores a fluctuating stock return to equilibrium.

The researchers, K. Ahn and coauthors, have published a paper on their application of a quantum harmonic oscillator to the dynamics of stock returns in a recent issue of EPL. One advantage of quantum models over traditional ones is that they are often better at incorporating the effects of market conditions on stock returns, which arises from how the quantum models account for the particles' energy levels.

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This leads to more accurate modeling overall. In the new study, the researchers focused on modeling a particular market force that has been difficult to capture in previous models.

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Empirical evidence shows that, when a stock return is fluctuating in the short term, there exists a market force that draws the fluctuating stock return back to its long-run equilibrium. This force is related to the concept of mean reversion, which is the tendency of a stock to return to its average price.

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In classical physics, a harmonic oscillator is a system that swings like a pendulum away from its equilibrium but has a restoring force that returns it to equilibrium. The quantum analogue, a quantum harmonic oscillator, is also a system that is displaced from equilibrium and has a restoring force, but has some differences compared to the classical system, such as that its energy levels are quantized discrete.

In their paper, the researchers show that the restoring force in a quantum harmonic oscillator can approximate the market force that returns a fluctuating stock return to equilibrium. By applying their model to seven years of data from the Financial Times How to apply quantum physics to trading Exchange All Share Index a subset of companies traded on the London Stock Exchangethey show that the quantum harmonic oscillator model outperforms other quantum models.

In this framework, the collective trading activities of the investors can be thought of as pressure on the stock prices, and the amount of pressure corresponds to the energy level of how to apply quantum physics to trading oscillating particle.

This article was co-authored by Dr. Roitman earned a Ph. How much leverage should we let homebuyers have?

A higher market uncertainty is equivalent to a higher energy level, but the volatility is limited by the financial equivalent of a high energy threshold. According to the model, the volatility eventually returns to some equilibrium level.

The researchers expect that the ability to accurately model stock market dynamics has potential applications for asset pricing, risk management, and asset allocation purposes. The results here might also be applied to comparing stock returns in different markets or different types of portfolios, as well as modeling the interest rate in the bond market.

Third, we are considering to apply our model further to risk management and asset allocation, such as value-at-risk.

Many of the problems facing the finance community have no known analytical solution. As a result, numerical methods and computer simulations for solving these problems have proliferated. This research area is known as computational finance.

Ahn et al. DOI: Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.