| Summary: | A topical issue in financial economics is the development of appropriate stochastic dynamic models for banking items and behavior. The issue here is to fulfil the need to generalize the more traditional discrete-time models of banking activity to a Levy process setting. In this thesis, under the assumption that the loan market is imperfectly competitive, we investigate the evolution of banking items such as bank assets (cash, bonds, shares, Treasuries, reserves, loans and intangible assets), liabilities (demand deposits) and bank capital (bank equity, subordinate debt and loan loss reserves). Here we consider the influence of macroeconomic factors and profitability as well as its indicators return on assets (ROA) and return on equity (ROE).
As far as bank assets are concerned, we note that loan pricing models usually reflect the financial funding cost, risk premium to compensate for the risk of default by the borrower, a premium reflecting market power exercised by the bank and the sensitivity of the cost of capital raised to changes in loans extended. On the other hand, loan losses can be associated with an offsetting expense called the loan loss provision (LLP), which is charged against Nett profit. This offset will reduce reported income but has no impact on taxes, although when the assets are finally written off, a tax-deductible expense is created. An important factor influencing loan loss provisioning is regulation and supervision. Measures of capital adequacy are generally calculated using the book values of assets and equity. The provisioning of loans and their associated write-offs will cause a decline in these capital adequacy measures, and may precipitate increased regulation by bank authorities. Greater level of regulation generally entail additional costs for the bank. Currently, this regulation mainly takes the form of the Basel II Capital Accord that has been implemented on the worldwide basis since 2008.
It is clear that bank profitability is a major indicator of financial crises for households, companies and financial institutions. An example of this from the 2007-2008 subprime mortgage crisis (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 29 September 2008. A further example from the SMC is that both the failure of the Lehman Brothers investment bank and the acquisition in September 2008 of Merrill Lynch and Bear Stearns by Bank of America and JP Morgan Chase, respectively, were preceded by a decrease in profitability and an increase in the price of loans and loan losses. The subprime mortgage crisis is characterized by contracted liquidity in the global credit markets and banking system. The level of liquidity in the banking sector affects the ability of banks to meet commitments as they become due without incurring substantial losses from liquidating less liquid assets. Liquidity, therefore, provides the defensive cash or near-cash resources to cover banks' liability. An undervaluation of real risk in the subprime market is cascading, rippling and ultimately severely adversely affecting the world economy. The downturn in the U.S. housing market, risky lending and borrowing practices, and excessive individual and corporate debt levels have caused multiple adverse effects tumbled as the US housing market slumped. Banks worldwide are hoarding cash and showing a growing reluctance to lend, driving rates that institutions charge to each other on loans to record highs. Also, global money markets are inoperative, forcing increased injections of cash from central banks. The crisis has passed through various stages, exposing pervasive weaknesses in the global financial system and regulatory framework.
The stochastic dynamics of the aforementioned banking items assist in formulating a maximization problem that involves endogenous variables such as profit consumption, the value of the bank's investment in loans and provisions for loan losses as control variants. In particular, we demonstrate that the bank is able to maximize its expected utility of discounted profit consumption over a random time interval, [t,r], and terminal profit at time r. Here the term profit consumption refers to the consumption of the bank's profits by dividend payments on equity and interest and principal payments on subordinate debt. The associated Hamilton-Jacobi-Bellman (HJB) equation has a smooth solution when the optimal controls are computed by means of power, logarithmic and exponential utility functions. This enables us to make a direct comparison between the economic properties of the solutions for different choices of the utility function.
In keeping with the main theme of this thesis, we simulate the financial indices ROE and ROA that are two measures of bank profitability. We further discuss optimization with power utility where we show the convergence of the Markov Chain Approximation Method (MCAM) and the impact of varying the model parameters in the form of loan loss severity, P, and loan loss frequency, <f>. We investigate the connections between the banking models and Basel II capital accord as well as the current subprime mortgage crises. As a way of conclusion, we provide remarks about the main issues discussed in the thesis and speculate about future research directions.
The contents of this thesis is based on 3 peer-reviewed journal articles (see [105], [106] and [107]) and 1 peer-reviewed conference proceedings paper (see [104]). In addition, the paper [108] is currently being prepared for submission to an accredited journal. === Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2009.
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