Quantum computational quantitative trading: high-frequency statistical arbitrage algorithm

Abstract

Quantitative trading is an integral part of financial markets with high calculation speed requirements, while no quantum algorithms have been introduced into this field yet. We propose quantum algorithms for high-frequency statistical arbitrage trading by utilizing variable time condition number estimation and quantum linear regression. The algorithm complexity has been reduced from the classical benchmark O ( N ^2 d ) to $O(\sqrt{dN}{\kappa }_{0}^{2}\,\mathrm{log}{(1/{\epsilon})}^{2})\left.\right)$ , where N is the length of trading data, and d is the number of stocks, κ _0 is the condition number and ϵ is the desired precision. Moreover, two tool algorithms for condition number estimation and cointegration test are developed.

Keywords

• quantum computation
• statistical arbitrage
• quantitative trading
• quantum finance