In the diploma thesis, we are first introduced to options and their meaning. The focus is on European stock options and we learn about the Black-Scholes formula which gives us the value of these options in the Black-Scholes model of the financial market. The model is determined by the stock price, its volatility, and the risk-free interest rate. Later, we learn about the effects of various market variables on changes in the value of the European option. Option Greeks describe these effects approximately. We derive the values of the best-known option Greeks and take a look at their application in practice. With their help, we optimize the portfolio in terms of risk mitigation (hedging). We then look at two basic hedging strategies and compare them as different market events happen. Finally, we look at how traders use hedging to trade implied volatility and how they make money when their prediction about the evolution of implied volatility is correct.
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