Weilian Shi: Distribution of Realized Volatility of Long Financial Time Series

Adviser: Prof. Dr. Werner Stahel

Co-Adviser: Dr. Michel Dacorogna

February 2011

Abstract:

Insurance companies face a difficult situation as the regulators ask for the same level of solvency during the crisis [Zumbach et al., 2000]. This master thesis focuses on the log returns and volatilities of very long financial time series. We investigate the distributions and tail behaviors of both log return and volatilities, where the Hill estimator is used for the tail index estimation of the volatility distribution. Taking the definition that a crisis occurs when the GDP consecutive drops for two quarters, the financial crisis has been identified as the biggest crisis after the Second World War. A linear regression model is conducted to analyze the connection between realized volatilities and the GDP log return before and after 1947, respectively. The negative correlation between them suggests that the volatility has the tendency to increase when the economy is experiencing a recession.

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