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The Black-Scholes Formula

Chapter 1:

Shall introduce the research questions and provide a very brief historical account of the Black Scholes Model.

So in summary the Black Scholes model can provide a description of the behaviour of an asset price but it is only an approximation. The plus side of this is that it can set a decent benchmark against which other models can be compared. In order to calculate the volatility, which is a crucial parameter for option pricing, a stochastic volatility model must be incorporated to account for the time varying volatility. These models aim to reflect apparent randomness of the level of volatility To a certain extent stochastic volatility models are consider successful and they can somewhat explain some of the biases present in the Black Scholes formula.

Both diffusion models and Garch models are widely used in the financial community, along with the incorporated stochastic volatility model they can account for phenomena such as volatility smiles (to be discussed in expanded report) mentioned previously in this report. They are considered to be a vast improvement for the BS model.

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