OPTIMAL INVESTMENT STRATEGY AND CAPITAL MANAGEMENT IN A BANK UNDER STOCHASTIC INTEREST RATE AND STOCHASTIC VOLATILITY

  • Theophilus Danjuma
  • H. C. Chinwenyi
  • Richard K. Tyokyaa
Keywords: Financial Institution, Investment Strategy, Stochastic Optimization Theory, Stochastic Interest Rate, Stochastic Volatility

Abstract

In this research work, we have looked at how a financial institution can optimally allocate its wealth among three assets namely: treasury, security and loan, and also manage it assets in stochastic interest rate and stochastic volatility setting. We derived the optimal investment policy through the application of dynamic programming principle for the case of constant relative risk aversion (CRRA) utility function. Furthermore, we derived the Stochastic Differential Equation (SDE) for the capital adequacy ratio under Basel Accord, the SDE for the Total Risk – Weighted Assets (TRWA), SDE for the capital required to maintain the capital adequacy ratio under Basel II and Central Bank of Nigeria (CBN) standards and solve the SDEs numerically to study how the financial institution can manage its assets. We also presented numerical examples to illustrate the dynamics of the optimal investment policy, TRWA SDE and SDE of the capital required to maintain the capital adequacy ratio under Basel II and Nigeria CBN standards.

References

Basel Committee on Banking Supervision (2004). International Convergence of Capital Measurements and Capital Standard: A revised Framework. Bank for International Settlements. www.bis.org/bcbs

Debajyoti, G. R., Bindya, K. and Swati, K. (2013). Basel I to Basel II to Basel III: A risk management journey in Indians Banks. AIMA Journal of Management and Research. 7(2/4): 474 – 497.

Dangl, J. P. and Lehar, B. (2004). Value at risk vs. building block regulation in banking. Journal of Financial Intermediation. 13: 132 – 155.

Decamps, J. P., Rochet, J. C. and Roger, B. (2004). The three pillars of Basel II: Optimizing the mix. Journal of Financial Intermediation. 13: 96 – 131.

Deelstra, G., Grasselli, M. and Koehl, P. F. (2003). Optimal investment strategies in the presence of a minimum guarantee. Insurance: Mathematics and Economics. 33: 189 – 207.

Diamond, D.W. and Rajan, R.G. (2000). A theory of bank capital. The Journal of Finance. 55(6): 2431 – 2465.

Fouche, C. H., Mukuddem – Petersen, J. and Petersen, M. A. (2006). Continuous – time stochastic modeling of capital adequacy ratio for banks. Applied Stochastic Model in Business and Industry. 22(1): 41 – 71.

Grant, E. M. and Peter, J. W. (2014). An optimal portfolio and capital management strategy for Basel III Compliant Commercial Banks. Journal of Applied Mathematics. Vol. 2014, Article ID 723873, 11 pages.

Hui, Z., Ximm, R. and Yonggan, Z. (2013). Optimal excess – of – loss reinsurance and investment problem for an insurer with jump – diffusion risk process under Heston model. Insurance: Mathematics and Economics. 53: 504 – 514.

Investopedia (2019). Basel Accord. Available at http://www.investopedia.com/items/b/basel_accord.asp (Accessed 27 November 2019).

Mukuddem – Petersen, J. and Petersen, M. A. (2008). Optimizing asset and capital adequacy management in banking. Journal of Optimization Theory and Applications. 137(1): 205 – 230.

Munk, C., Sorensen, C. and Vinther, T. N. (2004). Dynamic asset allocation under mean – reverting returns, stochastic interest rates and inflation uncertainty. Are popular recommendations consisted with rational behavior? International Review of Economics and Finance. 13: 141 – 166.

Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: The continuous case. Review of Economics and Statistics. 51: 247 – 257.

Merton, R. C. (1971). Optimal consumption and portfolio rules in a continuous time model. Journal of Economics Theory. 3: 373 – 413.

Peter, J. W., Garth, J. V. S. and Grant, E. M. (2011). An optimal investment strategy in bank management. Mathematical Methods in the Applied Sciences. 34: 1606 - 1617.

Von Thadden, E. L. (2004). Bank capital adequacy regulation under the new Basel accord. Journal of Financial Intermediation. 13(2): 90 – 95.

Ugo Obi – Chukwu (2014). Meaning of Capital Adequacy Ratio as Defined by Central Bank of Nigeria. www.nairametrics.com

Wachter, J. A. (2002). Portfolio and consumption decisions under mean – reverting returns: An exact solution for complete markets. Journal of Financial and Quantitative Analysis. 37(1): 63 – 91.

Published
2020-04-14
How to Cite
DanjumaT., ChinwenyiH. C., & TyokyaaR. K. (2020). OPTIMAL INVESTMENT STRATEGY AND CAPITAL MANAGEMENT IN A BANK UNDER STOCHASTIC INTEREST RATE AND STOCHASTIC VOLATILITY. FUDMA JOURNAL OF SCIENCES, 4(1), 528 - 538. Retrieved from https://fjs.fudutsinma.edu.ng/index.php/fjs/article/view/78