Document Type : Research Article
Authors
University of Sfax
Abstract
This paper has potential implications for the management of the bank. We examine a bank capital structure with contingent convertible debt to improve financial stability. This type of debt converts to equity when the bank is facing financial difficulties and a conversion trigger occurs. We use a leverage ratio, which is introduced in Basel III to trigger conversion instead of traditional capital ratios. We formulate an optimization problem for a bank to choose an asset allocation strategy to maximize the expected utility of the bank's asset value. Our study presents an application of stochastic optimal control theory to a banking portfolio choice problem. By applying a dynamic programming principle to derive the HJB equation, we define and solve the optimization problem in the power utility case.The numerical results show that the evolution of the optimal asset allocation strategy is really affected by the realization of the stochastic variables characterizing the economy. We carried out a sensitivity analysis of risk aversion, time and volatility. We also reveal that the optimal asset allocation strategy is relatively sensitive to risk aversion as well as that the allocation in CoCo and equity decreases as the investment horizon increases. Finally, sensitivity analysis highlights the importance of dynamic considerations in optimal asset allocation based on the stochastic characteristics of investment opportunities.
Keywords
[2] Black, F., and Scholes, M., The pricing of options and corporate liabilities, Journal of political economy, 81(3), 637 654, (1973).
[3] Bosch, T., Mukuddem-Petersen, J., Petersen, M. A. and Schoeman, I. M., Optimalauditing in the banking industry, Optimal Control, 28, 173 189 (2007).
[4] Dai, M., Jiang, L., Li, P. and Yi, F., Finite horizon optimal investment and consumption with transaction costs, SIAM Journal on Control and Optimization, 48(2), 1134-1154 (2009).
[5] Deelstra, G., Grasselli, M. and Koehl, P. F., Optimal investment strategies in the presence of a minimum guarantee, Insurance: Mathematics and Economics, 33(1), 189-207(2003).
[6] Duffie, D., Fleming, W., Soner, H. M. and Zariphopoulou, T., Hedging in incomplete markets with HARA utility, Journal of Economic Dynamics and Control, 21(4-5), 753-782(1997).
[7] Flannery, M. J., No pain, no gain? Effecting market discipline via reverse convertible debentures, Capital adequacy beyond Basel: Banking, securities, and insurance, 171-196(2005).
[8] Flannery, M.J, Stabilizing Large Financial Institutions with Contingent Capital Certicates, Available at SSRN: http://ssrn.com/abstract=1485689 (2009).
[9] Glasserman, P. and Wang, Z., Valuing the Treasury's Capital Assistance Program, Federal Reserve Bank of New York Staff Report No, 413, (2009).
[10] Hackbarth, D., Miao, J. and Morellec, E., Capital structure, credit risk and macroeconomic conditions, Journal of Financial Economics, 82(3), 519 550 (2006).
[11] Korn, R. and Kraft, H., A stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40(4), 1250-1269 (2002).
[12] Kronborg, M. T. and Steffensen, M., Inconsistent investment and consumption problems, Applied Mathematics and Optimization, 71(3), 473 515 (2015).
[13] McDonald, R. L., Contingent capital with a dual price trigger, Journal of Financial Stability,9(2), 230-241 (2013).
[14] Merton, R. C., Lifetime portfolio selection under uncertainty: The continuous-time case, The review of Economics and Statistics, 247-257 (1969).
[15] Merton, R. C., Optimum consumption and portfolio rules in a continuous-time model, In Stochastic optimization models in nance (pp. 621-661), Academic Press (1975).
[16] Mukuddem-Petersen, J. and Petersen, M. A., Bank management via stochastic optimal control, Automatica, 42, 1395 1406, MR2242924 (2006).
[17] Mukuddem-Petersen, J. and Petersen, M. A., Optimizing asset and capital adequacy management in banking, Journal of Optimization Theory and Applications, 137(1), 205-230(2008).
[19] Raviv, A., Bank Stability and Market Discipline: Debt-for-Equity Swap versus Subordinated Notes, Available at SSRN: http://ssrn.com/abstract=575862 (2004).
[20] Repullo, R., Capital requirements, market power, and risk-taking in banking, Journal of nancial Intermediation, 13(2),156-182 (2004).
[21] Squam Lake Working Group, An Expedited Resolution Mechanism for Distressed Financial Firms: Regulatory Hybrid Securities, Council on Foreign Relations (2009).
[22] Sundaresan, S. and Wang, Z., On the design of contingent capital with a market trigger, The Journal of Finance, 70(2), 881-920 (2015).
[23] Vila, J. L. and Zariphopoulou, T., Optimal consumption and portfolio choice with borrowing constraints, Journal of economic theory, 77(2), 402-431 (1997).
[24] Yao, R. and Zhang, H. H., Optimal consumption and portfolio choices with risky housing and borrowing constraints, The Review of Financial Studies, 18(1), 197-239 (2005).
[25] Zhao, Q., Shen, Y. and Wei, J., Consumption investment strategies with non-exponential discounting and logarithmic utility, European Journal of Operational Research, 238(3), 824835 (2014).
)