Discrete dynamics of bank credit and capital and their cyclicality

Thesis (M.Sc. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2009.With the unravelling of the global subprime mortgage crisis (SMC) in 2007 and 2008 and the worldwide implementation of new banking regulation in the form of the Basel II Capital Accord, issues related to bank valuation and profitability have become even more topical. It is widely recognized that the new capital (the Basel II) accord will improve the prevention of individual bank failures; however concern has been expressed about some unintended consequences. These include issues such as procyclicality, changes in bank lending behavior and the ability of supervisors to regulate banks that use more sophisticated risk management techniques, among others. A motivation for studying profitability is the fact that it is a major indicator of financial crises for households, companies and financial institutions. An example of this from the SMC is the U.S. bank, Wachovia Corp., who reported a big loss as from the first quarter of 2007 and eventually was bought by the world's largest bank, Citigroup, on Monday, 29 September 2008. In this dissertation, a first specific aim is to determine the value of a bank subject to Basel I and II capital requirements based on premiums for market, credit and operational risk. In order to accomplish this, we investigate the discrete-time dynamics of bank items such as assets, capital and bank profit when loan losses and macroeconomic conditions are explicitly considered. These models enable us to formulate an optimal bank valuation problem subject to cash flow, loan demand, financing and balance sheet constraints. However in the Basel I, we assume that risk-weights are constant. We also discuss the response of bank loans in the influence of the changes in the business cycle. Here operational risk is not considered as in the Basel II. Furthermore, we obtain results for the situation where loan losses and loan risk-weights are a function of the phases of the business cycle (i.e., risk-weights vary within the business cycle). In this regard, the main achievement of this dissertation is the discrete-time maximization of bank value via optimal choices of loan rate and supply, This process leads to the establishment of corresponding optimal deposits, provisions for deposit withdrawals and bank profitability, as in [51]. The choice of the aforementioned loan rate provides a connection with the SMC and subsequent credit crunch. Some of our findings are corroborated by considering empirical data sourced from the South African Reserve Bank (SARB). Here, we consider the output gap as a proxy of the changes in the business cycle and the cyclically of bank credit and capital. We present the output gap vs. the business cycle in order to demonstrate that the output gap is a real proxy of the changes in the business cycle.Master