A Comparative Predicting Stock Prices using Heston and Geometric Brownian Motion Models

Paper: arXiv 2302.07796

Authors: H. T. Shehzad, M. A. Anwar, M. Razzaq

Abstract

This paper presents a novel approach to predicting stock prices using technical analysis. By utilizing Ito’s lemma and Euler-Maruyama methods, the researchers develop Heston and Geometric Brownian Motion models that take into account volatility, interest rate, and historical stock prices to generate predictions. The results of the study demonstrate that these models are effective in accurately predicting stock prices and outperform commonly used statistical indicators. The authors conclude that this technical analysis-based method offers a promising solution for stock market prediction.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper applies standard stochastic calculus tools like Ito’s Lemma and Euler-Maruyama discretizations to standard financial models (GBM and Heston), but lacks true novelty as these are foundational textbook techniques. The empirical evaluation relies on framing continuous-time diffusion models as predictive ’technical analysis’ tools, which is conceptually weak and lacks rigorous modern backtesting protocols.

Research Flowchart

  flowchart TD
    A[Research Goal: Predict Stock Prices & Compare Models] --> B[Data Inputs: Historical Prices, Interest Rate & Volatility]
    B --> C[Mathematical Framework: Ito's Lemma]
    C --> D[Numerical Simulation: Euler-Maruyama Method]
    D --> E[Model Execution: Heston vs. Geometric Brownian Motion]
    E --> F[Outcomes: Models accurately predict prices & outperform statistical indicators]