In risk management it is very important to assess how financial instruments are distributed. For a long time, it was assumed that the distribution of financial instruments is normal. Over time they have rejected this hypothesis through empirical evidence and are now leaning toward distributions with heavy tails. Compared with normal distribution, deviations from average value are higher for heavy-tailed distributions. This means that in a normal distribution, it is less likely that an extreme event will occur. In the period after the financial crisis in 2009, financial institutions have become even more attentive to the risks brought about by extreme events. These extreme losses that occured during the crisis raised questions about the appropriateness and correctness of risk management models, which are mostly based on normal distribution. Due to the growing evidence that financial instruments are distributed with heavy-tailed distributions, emphasis has been placed on modeling heavy tails and on upgrading models for modeling extreme events. The goal of my thesis is to describe how heavy tails affect risk management and to present some of the methods that are often used in handling heavy tails. To illustrate, I will use different methods on the example of the NASDAQ index.
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