Speculative bubbles and the subsequent crashes are an integral part of human history. Greed and fear present in the financial markets naturally favor the occurrence of extreme events. Despite the research conducted for a long time in this topic, there is still no clear consensus on the definition and the causes of speculative bubbles. Their correct identification and forecasting in advance are still unresolved problems.

In my master's thesis I tried to answer the following questions: What are the speculative bubbles? What causes them? Is it possible to model market bubbles? How to diagnose bubbles ex-ante?

To answer these questions I used two practical models: Log-periodic power law and Generalized Hurst exponent. They were tested on 10 historical bubbles and then applied to the current situation on financial markets.

In this poster I'm describing my methods and showing the most important results. Especially interesting was detection of peak on DAX in April 2015, which was achieved in advance.

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1. Multifractal cross-correlation and casual direction between energy and financial markets in 2014-2016