The Black & Scholes formula and resulting advancements

This paper aims at deriving and interpreting the Black & Scholes formula with a special focus on the validity of the underlying assumptions and their effects on actual trading. This focus should bring about that the model`s properties become obvious, so that an ideal basis for a resulting evaluation is established. Thereby the original framework of Black & Scholes will be considered except for the last part where also advanced models will be discussed. The evaluation will be conducted on three levels, model-exogenously, model-endogenously and via a comparison with other models. At first the underlying assumptions will be contrasted by real market conditions, hereby it will be examined how crucial those assumptions are for the derivation of the formula and how closely they are interrelated. Secondly, a closer investigation of the argumentation used by Black & Scholes when deriving the formula will show how conclusive the model itself is. This includes an analysis of the model`s sensitivity to changes in the underlying parameters. Lastly, advanced models will be introduced to evaluate to which extent considering real market conditions can still be modeled within the framework of Black & Scholes or if completely new approaches are needed. This evaluation also follows the question if advanced models really provide any benefits for option pricing or if more precise values can only be optained in reverse for higher mathematical complexity.