This thesis applies functional data analysis techniques to address a number of specific research questions in financial markets. Data snooping bias controls are adopted in parallel to provide statistical robustness to our inferences. Firstly, we conduct an investigation into U.S. exchange-traded fund outperformance during the 2008-2012 period. The funds are tested for net asset value premium, underlying index and market benchmark outperformance. The study serves as a platform to showcase the data snooping bias problem and application of generalised multiple hypothesis testing techniques, in advance of their use for functional data analysis evaluation. Secondly, as the first application of functional data analysis, we examine implied volatility, jump risk, and pricing dynamics within crude oil markets. Strong evidence is found of converse jump dynamics during periods of demand and supply side weakness. Next, we demonstrate the performance advantage over traditional benchmarks of adopting a functional linear model to forecast EUR-USD implied volatility. Our findings are shown to be robust across various moneyness segments, contract maturities and out-of-sample window lengths. The final chapter also uses a functional data framework to produce forecasts, demonstrating how information can be extracted from forward contracts to predict future spot foreign exchange rates. The evaluation of an out-of-sample framework leads to near systematic outperformance in terms of a direct comparison of performance measures, versus both the restricted vector error correction model and random walk. Overall, this thesis highlights the usefulness of adopting insightful and novel functional data analysis techniques across various asset classes where multiple hypothesis testing controls provide robustness around our conclusions. Each of the studies contributes to the literature individually, with the collection emphasising the benefits of adopting functional approaches to tackle a wide range of empirical finance problems.