While being one of the most famous formulae in finance, it is also well-known that the assumptions of the Black and Scholes framework do not hold empirically. However, due to its beautiful analytic solution, the Black and Scholes formula is very widely used in option markets to describe option prices not in monetary units but in implied volatilities. In contrast to the Black and Scholes framework, which assumes those implied volatilities to be flat and constant, they are typically smileshaped and dynamic. As a consequence, the hedge ratios provided by the Black and Scholes framework are not capable to describe the relationship between changes in the underlying and changes in the option?s market value satisfyingly. This thesis aims to model the dynamics of the implied volatility surface of equity options in order to minimize the uncertainty of a delta-hedged option portfolio. While a lot of research has been done in the field of stochastic volatility models (e.g. Heston (1993)), only few studies examined empirical, model-free adjustments of Black and Scholes deltas. For that reason, we examine the existing, model-free adjustments and find that none of these approaches is capable to outperform the hedging performance of the Black and Scholes delta over the period between 1993 and 2006. Subsequently, we show the shortcomings of those adjustments and introduce another, more intuitive approach to model the implied volatility changes of a given option. We conclude by showing the superior performance of this approach, compared to the Black and Scholes delta, and suggest several extensions which might further improve the hedging performance.     «

While being one of the most famous formulae in finance, it is also well-known that the assumptions of the Black and Scholes framework do not hold empirically. However, due to its beautiful analytic solution, the Black and Scholes formula is very widely used in option markets to describe option prices not in monetary units but in implied volatilities. In contrast to the Black and Scholes framework, which assumes those implied volatilities to be flat and constant, they are typically smileshaped an...     »