Since the global financial crisis, there has been renewed focus on the analysis of sys- temic risk. Systemic risk refers to possibility that vulnerabilities across the financial system and between the financial system and the real economy will be triggered. As a result, intermediation activities may be curtailed and a financial crisis may occur. There are a number of aspects to systemic risk and related financial stability analy- sis. First, imbalances and risk can accumulate in both the financial system and in the composition of economic activity during an economic upswing, due to either adverse incentives or myopia by economic agents. Second, macro-financial linkages and conta- gion channels between financial intermediaries not only amplify potential risk during the boom period, but also exacerbate the economic impact when the cycle turns, or if there is an adverse shock. This thesis focuses on two current issues in financial stabil- ity research for the banking sector, namely the analysis of bank funding risk during a financial crisis and the detection of unsustainable property price movements. Funding risk and asset price bubbles, particularly in the commercial real estate market played a significant role in the origins of both the Irish and the global financial crisis. Across three chapters, this thesis presents original research on these topics using Irish data as a statistical example. Chapter one examines the determinants of weekly corporate deposit levels in Irish banks over the period March 2009 to August 2010. This sample includes the early stages of the Irish banking crisis, which began in 2008. The global financial crisis resulted in Irish banks experiencing more acute funding dificulties than institutions elsewhere. Using a unique high-frequency database and drawing on both the financial crisis and market discipline literature, the sensitivity of corporate depositors to move- ments in both idiosyncratic and systemic risk factors is tested. There is statistical evidence that measures of risk for the Irish banking sector such as implied ratings and credit default swap spreads can explain corporate deposit levels over the sample, val- idating the market discipline hypothesis. These results further provide an empirical link between counter-party credit risk and bank funding risks. Additionally, tensions in European inter-bank markets are found to negatively impact corporate deposits indicating contagion channels between funding markets during periods of systemic stress. The empirical relationship between daily corporate and retail deposits is also examined. Although retail deposit flows move in the same direction as corporate de- posits, retail deposits appear to exhibit relatively higher inertia up to August 2010. Chapter one has been re-drafted from a co-authored policy-orientated research paper with Kieran McQuinn which is available as a Central Bank of Ireland Research Tech- nical Paper (No.2/12) entitled "Modelling the corporate deposits of Irish financial institutions: 2009-2010". Expanding the dataset to early-2014, chapter two models the dynamic behaviour of weekly customer deposits (i.e., both retail and corporate) held with Irish banks over the period March 2009 to end-December 2013 using an ARDL(1,1) - GARCH(1,1) framework. Over the sample, which covers the Irish systemic banking crisis, weekly customer deposit flows are found to respond to measures of banking sector and sovereign risk which is consistent with the theory of market discipline among de- positors. Although the data cover resident and non-resident depositors, idiosyncratic and Irish-specific risk factors seem to have more explanatory power for deposit growth. Indicators of general stress in international financial markets are found to be statisti- cally insignificant. Once market-based risk factors are included in the model, no direct macro-economic infuence is found. Over the sample, statistical evidence of a regime shift is found, with deposits switching from a high variance regime to a low variance regime with the onset of an EU/ECB/IMF Programme of assistance for Ireland in early-December 2010. Interestingly, evidence of a GARCH-in-Mean effect indicates that the conditional variance of customer deposits negatively affects deposit growth rates over the sample. An adverse reaction to risk as proxied by the conditional volatility would be consistent with fight-to-quality theories of deposit behaviour. Chapter three analyses price developments in the Irish commercial property mar- ket over the period 1985Q1 to 2012Q4 using time-series techniques. First, three dif- ferent statistical approaches are used to test if prices can be explained by fundamental determinants such as income, interest rates and credit. Evidence of some deviations between actual and fundamental prices over the sample period is found. Second, two popular models of price misalignment from the stock price literature are used to test whether these estimated misalignments between actual prices and fundamentals (i.e., non-fundamental prices) suggest that there is an irrational fad or a rational bubble in Irish commercial property prices over the period under study. To distinguish between these two models, regime switching methodology is used. The study funds evidence of a number of periods where commercial property prices deviate from fundamentally determined values for a sustained period. The periods of estimated misalignment are found to be broadly consistent across the various approaches. In testing between a rational bubble and the irrational fad hypothesis, evidence of regime shifts over the sample provide some support for the presence of a bubble. However, the point es- timates of expected returns in each regime are not fully in-line with the theoretical predictions of the rational bubble theory. Therefore, the results are not conclusive in favour of the rational bubble hypothesis.