The Black & Scholes formula and resulting advancements

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This paper derives and interprets the Black & Scholes formula, emphasizing the validity of its underlying assumptions and their impact on actual trading. The aim is to clarify the model's properties, establishing a solid foundation for evaluation. The original Black & Scholes framework will be considered, with advanced models discussed later. Evaluation occurs on three levels: model-exogenous, model-endogenous, and through comparisons with other models. Initially, the assumptions will be compared to real market conditions to assess their importance in deriving the formula and their interrelations. Next, a detailed examination of Black & Scholes' argumentation will reveal the model's conclusiveness, including an analysis of its sensitivity to changes in underlying parameters. Finally, advanced models will be introduced to determine how well they accommodate real market conditions within the Black & Scholes framework or if entirely new approaches are necessary. This evaluation will also address whether advanced models genuinely enhance option pricing or if more accurate values come at the cost of increased mathematical complexity.