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