<p>In Black-Scholes model, the parameters -a volatility and an interest rate were assumed as constants. In this thesis we concentrate on behaviour of the volatility as</p><p>a function and we find more realistic models for the volatility, which elimate a risk</p><p>connected with behaviour of the volatility of an underlying asset. That is</p><p>the reason why we will study the Uncertain Volatility Model. In Chapter</p><p>1 we will make some theoretical introduction to the Uncertain Volatility Model</p><p>introduced by Avellaneda, Levy and Paras and study how it behaves in the different scenarios. In</p><p>Chapter 2 we choose one of the scenarios. We also introduce the BSB equation</p><p>and try to make some modification to narrow the uncertainty bands using</p><p>the idea of a static hedging. In Chapter 3 we try to construct the proper</p><p>portfolio for the static hedging and compare the theoretical results with the real</p><p>market data from the Stockholm Stock Exchange.</p>

In Black-Scholes model, the parameters -a volatility and an interest rate were assumed as constants. In this thesis we concentrate on behaviour of the volatility as a function and we find more realistic models for the volatility, which elimate a risk connected with behaviour of the volatility of an underlying asset. That is the reason why we will study the Uncertain Volatility Model. In Chapter 1 we will make some theoretical introduction to the Uncertain Volatility Model introduced by Avellaneda, Levy and Paras and study how it behaves in the different scenarios. In Chapter 2 we choose one of the scenarios. We also introduce the BSB equation and try to make some modification to narrow the uncertainty bands using the idea of a static hedging. In Chapter 3 we try to construct the proper portfolio for the static hedging and compare the theoretical results with the real market data from the Stockholm Stock Exchange.