Bank Liquidity and the Global Financial Crisis

Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2012, Article ID 743656, 27 pages doi:10.1155/2012/743656 Research Article Bank Liquidity and the Global Financial Crisis Frednard Gideon,1 Mark A. Petersen,2 Janine Mukuddem-Petersen,3 and Bernadine De Waal2 1 Department of Mathematics, Faculty of Science, University of Namibia, Private Bag 13301, Windhoek 9000, Namibia 2 Research Division, Faculty of Commerce and Administration, North-West University, Private Bag x2046, Mmabatho 2735, South Africa 3 Economics Division, Faculty of Commerce and Administration, North-West University, Private Bag x2046, Mmabatho 2735, South Africa Correspondence should be addressed to Frednard Gideon, Received 2 November 2011; Revised 22 January 2012; Accepted 5 February 2012 Academic Editor: Chuanhou Gao Copyright q 2012 Frednard Gideon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the stochastic dynamics of bank liquidity parameters such as liquid assets and nett cash outflow in relation to the global financial crisis. These parameters enable us to determine the liquidity coverage ratio that is one of the metrics used in ratio analysis to measure bank liquidity. In this regard, numerical results show that bank behavior related to liquidity was highly procyclical during the financial crisis. We also consider a theoretical-quantitative approach to bank liquidity provisioning. In this case, we provide an explicit expression for the aggregate liquidity risk when a locally risk-minimizing strategy is utilized. 1. Introduction During the global financial crisis GFC, banks were under severe pressure to maintain adequate liquidity. In general, empirical evidence shows that banks with sufficient liquidity can meet their payment obligations while banks with low liquidity cannot. The GFC highlighted the fact that liquidity risk can proliferate quickly with funding sources dissipating and concerns about asset valuation and capital adequacy realizing. This situation underscores the important relationship between funding risk involving raising funds to bankroll asset holdings and market liquidity involving the efficient conversion of assets into liquid funds at a given price. In response to this, the Basel Committee on Banking Supervision BCBS is attempting to develop an international framework for liquidity risk measurement, standards, and monitoring see, e.g., 1. Although pre-Basel III regulation 2 Journal of Applied Mathematics establishes procedures for assessing credit, market, and operational risk, it does not provide effective protocols for managing liquidity and systemic risks. The drafting of Basel III represents an effort to address the latter see, e.g., 2–4. Current liquidity risk management procedures can be classified as micro- or macroprudential. In the case of the former, simple liquidity ratios such as credit-to-deposit ratios nett stable funding ratios, liquidity coverage ratios and the assessment of the gap between short-term liabilities and assets are appropriate to cover the objectives of bank balance sheet analysis. The ratio approach for liquidity risk management is a quantitative international accepted standard for alerting banks about any possible adverse economic downturns. For instance, the credit-to-deposit ratio assesses the relationships between sources and uses of funds held in the bank’s portfolio but has limitations which ultimately do not reflect information on market financing with short-term maturity. By contrast, the liquidity coverage ratio LCR performs better by ensuring the coverage of some of the immediate liabilities. Since the LCR depends only on bank balance sheet data, it does not take into account the residual maturities on various uses and sources of funds. Also, in a global context, a quantitative approach may not take financial market conditions into account. In this case, a more comprehensive characterization of the bank system’s liquidity risk through designed stress testing and constructed contingency plans is considered. The Basel Committee on Banking Supervision suggested best practices related to international liquidity standards. In this case, a well-designed policy monitoring instrument to measure and regulate the dynamics of foreign currency is considered to best take financial market conditions into account. Also, central banks CBs have a pivotal role to play in managing liquidity inflows via macroeconomic management of exchange rate and interest rate responses. The modeling of capital markets as well as stock and bond behavior also contribute to the liquidity response for possible stress conditions observed. The above approaches for liquidity analysis take into account the macroprudential liquidity management of banks. In this paper, in Section 2, we discuss balance sheet items related to liquid assets and nett cash outflow in order to build a stochastic LCR model. Before the GFC, banks were prosperous with high LCRs, high cash inflows, low interest rates, and low nett cash outflows. This was followed by the collapse of liquidity, exploding default rates, and the effects thereof during the GFC. Next, in Section 3, we apply a dynamic provisioning strategy to liquidity risk management. In this case, we address the problem of dynamic liquidity provisioning for a mortgage, Λ, which is an underlying illiquid nonmarketable asset, by substituting liquid marketable securities, S. In the light of the above, banks prefer to trade in a Treasury bond market because of liquidity reasons. Since the loan process Λt 0≤t≤T is not completely correlated with the substitute, it creates the market incompleteness. In other words, we will employ non-self-financing strategy to replicate the trading process. Therefore the banks would require that the uncertainty involved over the remaining of the trading period be minimized. In this case, we specifically minimize at each date, the uncertainty over the next infinitesimal period. In the dynamics trading there is always a residual risk emanating from the imperfection of the correlation between the Brownian motions. Due to the no-arbitrage opportunities there are infinitely many equivalent martingale measures so that pricing is directly linked to risk. Therefore, we choose a pricing candidate equivalent martingale measure under which the discounted stock price follows a martingale. This equivalent measure is chosen according to a provisioning strategy which ensures that the value of Λ is the value of the replicating portfolio. We also provide a framework for assessing residual aggregate liquidity risk stemming from the application of the above strategy. Journal of Applied Mathematics 3 1.1. Literature Review The documents formulated in response to the proposed Basel III regulator (...truncated)