  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.
