New developments in econophysics: Option pricing formulas

Paper: arXiv 2301.11078

Authors: Moawia Alghalith

Abstract

We synthesize and discuss some new developments in econophysics. In doing so, we focus on option pricing. We relax the assumptions of constant volatility and interest rate. In doing so, we rely on the square root of the Brownian motion. We also provide simple, closed-form pricing formulas for the American and Bermudan options.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper attempts theoretical advances by introducing non-constant volatility and interest rate processes via Brownian motion square-root derivations for option pricing. However, it lacks robust empirical validation, real-world data backtesting, or statistical verification of the proposed closed-form solutions.

Research Flowchart

  flowchart TD
    A[Research Goal: Advance Econophysics Option Pricing] --> B[Input: Square Root of Brownian Motion]
    B --> C[Relax Assumptions: Non-constant Volatility & Interest Rates]
    C --> D[Develop Closed-Form Pricing Formulas]
    D --> E[Outcome: Pricing Formulas for American Options]
    D --> F[Outcome: Pricing Formulas for Bermudan Options]