Integration of Fractional Order Black-Scholes Merton with Neural Network

ArXiv ID: 2310.04464 “View on arXiv”

Authors: Unknown

Abstract

This study enhances option pricing by presenting unique pricing model fractional order Black-Scholes-Merton (FOBSM) which is based on the Black-Scholes-Merton (BSM) model. The main goal is to improve the precision and authenticity of option pricing, matching them more closely with the financial landscape. The approach integrates the strengths of both the BSM and neural network (NN) with complex diffusion dynamics. This study emphasizes the need to take fractional derivatives into account when analyzing financial market dynamics. Since FOBSM captures memory characteristics in sequential data, it is better at simulating real-world systems than integer-order models. Findings reveals that in complex diffusion dynamics, this hybridization approach in option pricing improves the accuracy of price predictions. the key contribution of this work lies in the development of a novel option pricing model (FOBSM) that leverages fractional calculus and neural networks to enhance accuracy in capturing complex diffusion dynamics and memory effects in financial data.

Keywords: Option Pricing, Fractional Black-Scholes-Merton, Neural Networks, Fractional Calculus, Stochastic Volatility, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper presents complex mathematical formulations involving fractional calculus (Riemann-Liouville derivatives) and PDEs, indicating high mathematical density. However, the excerpt shows no actual implementation, backtesting, or validation against real market data, relying solely on theoretical assertions.

  flowchart TD
    A["Research Goal: Enhance option pricing accuracy by integrating fractional calculus with neural networks"] --> B["Data & Inputs: Historical Option Market Data & Stochastic Parameters"]
    B --> C["Methodology: FOBSM with Neural Network Hybridization"]
    C --> D{"Computational Process"}
    D --> E["Fractional Derivatives: Model Memory Effects in Sequences"]
    D --> F["NN Training: Capture Complex Diffusion Dynamics"]
    E & F --> G["Synthesis: Hybrid FOBSM-NN Model"]
    G --> H["Key Outcomes: Improved Pricing Accuracy & Authenticity"]