Application of Game Theory in Option Pricing: A Binomial Tree Model Approach

Zheming Bao

2024

Abstract

This study combines game theory, specifically Nash equilibrium, with binomial tree models to analyze and predict options pricing for Apple Inc. (AAPL). Using historical stock price and option data from January 1, 2022 to January 1, 2023, a model is constructed to simulate potential future stock prices and determine the optimal strategy for option execution. The model calculates historical volatility and uses it to create a detailed binomial tree, while the return matrix is derived from stock price movements and option strike prices. Then the Nash equilibrium strategy is calculated by linear programming. Back-testing results show that the strategy effectively identifies profitable opportunities, especially in volatile market conditions. Although the model relies on assumptions such as constant volatility and risk-free interest rates, the findings highlight its practical applicability to financial decision making. This approach provides a robust framework for further research, with the potential to incorporate real-time data and extend to other stocks to improve the accuracy and reliability of option pricing analysis.

Paper Citation

in Harvard Style

Bao Z. (2024). Application of Game Theory in Option Pricing: A Binomial Tree Model Approach. In Proceedings of the 1st International Conference on Innovations in Applied Mathematics, Physics and Astronomy - Volume 1: IAMPA; ISBN 978-989-758-722-1, SciTePress, pages 174-178. DOI: 10.5220/0013009600004601

in Bibtex Style

@conference{iampa24,
author={Zheming Bao},
title={Application of Game Theory in Option Pricing: A Binomial Tree Model Approach},
booktitle={Proceedings of the 1st International Conference on Innovations in Applied Mathematics, Physics and Astronomy - Volume 1: IAMPA},
year={2024},
pages={174-178},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013009600004601},
isbn={978-989-758-722-1},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Innovations in Applied Mathematics, Physics and Astronomy - Volume 1: IAMPA
TI - Application of Game Theory in Option Pricing: A Binomial Tree Model Approach
SN - 978-989-758-722-1
AU - Bao Z.
PY - 2024
SP - 174
EP - 178
DO - 10.5220/0013009600004601
PB - SciTePress