A new measure of risk using Fourier analysis

TL;DR

This paper introduces a novel Fourier analysis-based measure to detect speculative risk in financial products by analyzing the frequency of price changes relative to company value, addressing previous methodological flaws.

Contribution

It presents a corrected and reliable Fourier analysis method for assessing risk in financial markets, applicable across a broad frequency spectrum, and demonstrates its effectiveness on stock data.

Findings

Stocks change disproportionately within one week indicating speculation

Fourier analysis effectively detects high-frequency trading activity

Method can be extended to analyze cryptocurrencies

Abstract

We use Fourier analysis to access risk in financial products. With it we analyze price changes of e.g. stocks. Via Fourier analysis we scrutinize quantitatively whether the frequency of change is higher than a change in (conserved) company value would allow. If it is the case, it would be a clear indicator of speculation and with it risk. The entire methods or better its application is fairly new. However, there were severe flaws in previous attempts; making the results (not the method) doubtful. We corrected all these mistakes by e.g. using Fourier transformation instead of discrete Fourier analysis. Our analysis is reliable in the entire frequency band, even for fre-quency of 1/1d or higher if the prices are noted accordingly. For the stocks scrutinized we found that the price of stocks changes disproportionally within one week which clearly indicates spec-ulation. It would be an interesting extension to apply the method to crypto currencies as these currencies have no conserved value which makes normal considerations of volatility difficult.