An analysis of capital market through the lens of integral transforms: exploring efficient markets and information asymmetry

ArXiv ID: 2506.06350 “View on arXiv”

Authors: Kiran Sharma, Abhijit Dutta, Rupak Mukherjee

Abstract

Post Modigliani and Miller (1958), the concept of usage of arbitrage created a permanent mark on the discourses of financial framework. The arbitrage process is largely based on information dissemination amongst the stakeholders operating in the financial market. The advent of the efficient market Hypothesis draws close to the M&M hypothesis. Giving importance to the arbitrage process, which effects the price discovery in the stock market. This divided the market as random and efficient cohort system. The focus was on which information forms a key factor in deciding the price formation in the market. However, the conventional techniques of analysis do not permit the price cycles to be interpreted beyond its singular wave-like cyclical movement. The apparent cyclic measurement is not coherent as the technical analysis does not give sustained result. Hence adaption of theories and computation from mathematical methods of physics ensures that these cycles are decomposed and the effect of the broken-down cycles is interpreted to understand the overall effect of information on price formation and discovery. In order to break the cycle this paper uses spectrum analysis to decompose and understand the above-said phenomenon in determining the price behavior in National Stock Exchange of India (NSE).

Keywords: Spectrum Analysis, Arbitrage Theory, Price Discovery, Efficient Market Hypothesis, Signal Decomposition, Equities

Complexity vs Empirical Score

• Math Complexity: 4.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Philosophers
• Why: The paper mentions integral transforms (Fourier) but provides no formulas, derivations, or computational details, suggesting low math complexity. Empirical work is described as using NSE tick data and simulation, but no backtest results, metrics, or implementation code are shown, indicating low rigor.

  flowchart TD
    A["Research Goal<br>Analyze price cycles & information<br>in NSE using integral transforms"] --> B["Data Inputs<br>NSE Equity Data (Price/Volume)<br>+ Market Information (News)"]
    B --> C["Methodology<br>Spectrum Analysis & Signal Decomposition<br>to break down price cycles"]
    C --> D["Computational Process<br>Apply Integral Transforms<br>to decompose price signals<br>into frequency components"]
    D --> E["Key Findings / Outcomes<br>1. Identified market regimes (Random/Efficient)<br>2. Quantified information impact on price discovery<br>3. Validated arbitrage efficiency via spectral analysis"]