On meeting capital requirements with a chance-constrained optimization model

Abstract

This paper deals with a capital to risk asset ratio chance-constrained optimization model in the presence of loans, treasury bill, fixed assets and non-interest earning assets. To model the dynamics of loans, we introduce a modified CreditMetrics approach. This leads to development of a deterministic convex counterpart of capital to risk asset ratio chance constraint. We pursue the scope of analyzing our model under the worst-case scenario i.e. loan default. The theoretical model is analyzed by applying numerical procedures, in order to administer valuable insights from a financial outlook. Our results suggest that, our capital to risk asset ratio chance-constrained optimization model guarantees banks of meeting capital requirements of Basel III with a likelihood of 95 % irrespective of changes in future market value of assets.

Satisfying Bank Capital Requirements: A Robustness Approach in a Modified Roy Safety-First Framework

“…The proposed asset-liability optimization model is based on constraint robustness with the chance constraint of capital to risk assets ratio in a safety-first framework under the condition that only moment information is known. This paper aims to extend the proposed single-objective capital to the risk asset ratio chance-constrained optimization model in [4] by considering the multi-objective constraint robustness approach in a modified safety-first framework.…”

“…This paper employs a modified CreditMetrics approach to estimate the future market value of loans, i.e., the uncertainty parameter in (1). A modified CreditMetrics approach has been proposed by [4]. We adopted this approach for the sole aim of determining the future market value of loans and the associated risk measure.…”

“…The utilization of CRAR safeguards depositors and improves the efficiency and stability of financial frameworks. In [4], a CRAR chance-constrained optimization model was proposed to guarantee that a bank can cope with the capital requirements of Basel III with a probability of 95%, irrespective of the changes in the future market value of assets. The proposed model considered loans having truncated Gaussian distributed returns, which allowed reformulating the chance constraint related to capital requirements in a second-order cone condition.…”

“…The work in [4] assumed that the full and accurate probability distribution of the random vector ζ is known, given estimations from historical data and information from the literature. However, one might have only partial information about the probability distribution: its moment information.…”

“…This paper aims to extend the proposed single-objective CRAR chance constrained optimization model in [4] by considering the multi-objective constraint robustness approach in a modified safety-first framework. This paper also considers credit risk and the expected value of the portfolio.…”