Stochastic Calculus and the Black-Scholes-Merton Model: A Simplified Approach

Paper: arXiv 2605.07558

Authors: Kuo-Ping Chang

Abstract

This paper refutes the claim that the expected rate of return of the underlying asset plays no role in the Black-Scholes-Merton option pricing model.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper attempts to challenge a fundamental concept in option pricing theory using standard stochastic calculus derivations. However, it lacks empirical validation, empirical data backtesting, and relies on a misunderstanding of risk-neutral pricing principles, limiting its contribution.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate role of expected rate of return in BSM model] --> B[Data Inputs: Underlying Asset Dynamics & Option Contracts]
    B --> C[Methodology: Apply Stochastic Calculus & Ito's Lemma]
    C --> D[Computational Process: Derive Geometric Brownian Motion Differential Equations]
    D --> E[Key Outcome: Refute claim that expected return plays no role in BSM]