Mathematical Foundations of Option Pricing Models: A Comparative Analysis
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This document presents a comprehensive mathematical analysis of three principal option pricing methodologies: Black-Scholes, Binomial Tree, and Monte Carlo simulation. Each section rigorously examines the theoretical underpinnings, derivation procedures, implementation considerations, and comparative advantages of these models. The analysis includes formal mathematical proofs, computational complexity assessments, and convergence properties. This documentation serves as both a theoretical reference and practical implementation guide for financial modeling practitioners.
