Entropy Analysis of Financial Time Series

This thesis applies entropy as a model independent measure to address three research questions concerning financial time series. In the first study we apply transfer entropy to drawdowns and drawups in foreign exchange rates, to study their correlation and cross correlation. When applied to daily and hourly EUR/USD and GBP/USD exchange rates, we find evidence of dependence among the largest draws (i.e. 5% and 95% quantiles), but not as strong as the correlation between the daily returns of the same pair of FX rates. In the second study we use state space models (Hidden Markov Models) of volatility to investigate volatility spill overs between exchange rates. Among the currency pairs, the co-movement of EUR/USD and CHF/USD volatility states show the strongest observed relationship. With the use of transfer entropy, we find evidence for information flows between the volatility state series of AUD, CAD and BRL. The third study uses the entropy of S&P realised volatility in detecting changes of volatility regime in order to re-examine the theme of market volatility timing of hedge funds. A one-factor model is used, conditioned on information about the entropy of market volatility, to measure the dynamic of hedge funds equity exposure. On a cross section of around 2500 hedge funds with a focus on the US equity markets we find that, over the period from 2000 to 2014, hedge funds adjust their exposure dynamically in response to changes in volatility regime. This adds to the literature on the volatility timing behaviour of hedge fund manager, but using entropy as a model independent measure of volatility regime.