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Exploring the Dynamics of Financial Derivatives: A Partial Differential Equation Approach to Option Pricing Models

LEBEDE Ngartera, NDOGOTAR Nelio, NGARKODJE Ngarasta

Abstract



This paper delves into the sophisticated realm of financial mathematics, exploring the pivotal role of partial differential equations (PDEs) in the intricate domain of option pricing. Central to this investigation is the renowned Black-Scholes equation and its multifaceted variants, which form the backbone of mathematical modeling for financial instruments across diverse market conditions. By harnessing advanced numerical techniques such as the Finite Volume Method and Monte Carlo simulations, this study reveals the profound complexities and dynamic behaviors intrinsic to PDE-based option pricing models. Additionally, it navigates the cutting-edge landscape of stochastic volatility models and jump-diffusion processes, highlighting their transformative impact on the modeling of complex market dynamics. Through this comprehensive exploration, we illuminate the intricate interactions within financial markets and outline a roadmap for future research directions. The paper aspires to bridge the gap between classical financial theories and modern computational advancements, ultimately enhancing the precision and applicability of mathematical finance.

Keywords


Option Pricing Models, Partial Differential Equations (PDEs), Financial Derivatives, Market Dynamics, Stochastic Volatility, Machine Learning

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