The first two chapters of the thesis are a comparative study of several methods for correlation estimation from high-frequency data. These range from the well established Pearson correlation coefficient and Spearman's rho to the more recently proposed realised correlation and Fourier method estimators. Measuring correlation from high-frequency data is impeded by two main problems. One problem stems from the asynchronous and non-homogeneous nature of the time series and the other is caused by a market microstructure effect called the "Epps effect". The performance of each correlation method in dealing with both problems is first assessed with simulated data and then with real time series spanning 14 years of trades in S&P1 00 stocks. The correlation matrices thus obtained are analysed with the aid of Random Matrix Theory and network analysis tools such as Minimum Spanning Trees. In the third chapter, network analysis tools are applied to the Italian interbank payments system. The objective is to analyse the network topology of the system in order to ascertain the differences in the activities of banks of different sizes and the evolution of their connectivity structure over time. This helps in assessing the stability of the banking system and the efficiency of the interbank market. The fourth chapter introduces a new class of stochastic processes called Ito semi-diffusions as an alternative modelling framework for asset price dynamics. These models provide a better fit for the distributional properties of asset prices whilst maintaining analytical tractability. Numerous examples are given together with an illustration of a pricing method for the valuation of contingent claims. In the final chapter a stochastic control problem that arises in the context of commodity storage valuation is considered. The model's operational characteristics can be associated with different types of inventories such as hydro-electric reservoirs or gas storage facilities. Under suitable assumptions, it is shown that the optimal storage strategy depends only on the planning horizon and on the amount of stored commodity but not on the actual commodity price.