A new measure of risk using Fourier analysis

ArXiv ID: 2408.10279 “View on arXiv”

Authors: Unknown

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.

Keywords: Fourier Analysis, Risk Analysis, Speculation, Price Volatility, Signal Processing, Equities

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats
  • Why: The paper introduces advanced mathematical concepts like Fourier transforms and provides some derivations, but lacks any implementation details, backtesting results, or statistical metrics, making it a theoretical exercise rather than an empirically rigorous quant finance study.
  flowchart TD
    A["Research Goal: Quantify speculation-based risk in financial assets"] --> B["Methodology: Fourier Analysis on price data"]
    B --> C["Input: Daily stock price time-series data"]
    C --> D["Process: Apply Fourier Transformation<br/>(vs. Discrete Analysis)"]
    D --> E["Analysis: Is signal frequency > fundamental value changes?"]
    E -- Yes --> F["Outcome: High Speculation Indicator<br/>(e.g., price changes > 1/week)"]
    E -- No --> G["Outcome: Stable/Intrinsic Valuation"]
    F --> H["Conclusion: Validated risk measure<br/>Extension: Crypto assets (no conserved value)"]
    G --> H