This thesis is structured in three chapters, each pertaining to a specific problem in financial economics. The first chapter, titled 'High-Frequency Jump Analysis of the Bitcoin Market' and co-authored with Prof. Olivier Scaillet and Adrien Treccani of the University of Geneva, studies the market for bitcoin, a pioneer virtual currency, and its price dynamics. Using data for all the trades that took place on the exchange Mt. Gox during the period June 2011 to November 2013, we analyse the occurrence of jumps in the price process and conclude that they are frequent (one jump per week, on average) and that they tend to cluster in time. They are predicted by the order flow imbalance and the preponderance of aggressive traders. Jumps have a short-term positive impact on market activity and illiquidity and see a persistent change in the price. The second chapter, titled 'Price Formation in the Bitcoin Market', studies the same bitcoin market from the point of view of information and the way it is incorporated in the price. I analyse different measures of liquidity and price impact and find that bitcoin exhibits more adverse selection than comparable stocks. I examine the potential profits of liquidity provision and conclude that they are insufficient, which explains the absence of market makers and consequently the low market depth. I estimate a vector autoregressive model for the returns and a trade indicator and find that the effect of past returns and past trades on contemporaneous trades is significant and singular, indicating that agents infer considerable information which leads them to update their beliefs about the future evolution of the price, consistent with the view that bitcoin is a Keynesian beauty contest. The third chapter, titled 'Cash Holdings and Credit Risk', investigates the a priori surprising empirical phenomenon that firms with larger cash holdings appear to be riskier with regards to the valuation of their debt. It is explained by the endogeneity affecting the relation between a firm's cash holdings and credit spread. Indeed, a firm facing more risk (for instance, because its cash flows are more volatile) will optimally choose larger cash holdings as a hedge. I review the related literature and present a class of continuous-time capital structure models capable of capturing this phenomenon.