American option in a market generated by interactive agents

Authors

  • Besma Hamidane
  • Nawel Arrar
  • Mohamed Riad Remita

DOI:

https://doi.org/10.54021/seesv5n1-163

Keywords:

complete market, incomplete market, european option, american option, risk neutral probability

Abstract

This study introduces a new financial market model inspired by Remita and Eisele's methodology, incorporating a substantial number of interacting agents denoted by “n”. Focusing on the valuation of European and American options within this vast network of agents, and more specifically on behavior when “n” tends to infinity, the research illustrates the convergence of an initially incomplete market towards completeness. In addition, the study scrutinizes the price stability of options on the underlying risky asset, St, in the context of an increasing number of agents. Taking into account a comprehensive set of internal and external factors influencing market dynamics, this study offers a holistic analysis of option price dynamics and market completeness. By examining the complex interactions between a large number of agents and option pricing, the research provides valuable insights into the complexity of financial markets. The results not only elucidate convergence phenomena within an expanding network of agents, they also shed light on the stability of option prices under ever-changing market conditions. This comprehensive analysis underlines the multifaceted nature of financial markets, highlighting the intrinsic relationship between option price dynamics and various market influences. Overall, this study makes a significant contribution to the understanding of financial market dynamics, particularly in the context of option pricing.

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Published

2024-06-24

How to Cite

Hamidane, B., Arrar, N., & Remita, M. R. (2024). American option in a market generated by interactive agents. STUDIES IN ENGINEERING AND EXACT SCIENCES, 5(1), 3286–3311. https://doi.org/10.54021/seesv5n1-163