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Continuous‐time stochastic modelling of capital adequacy ratios for banks
Author(s) -
Fouche Casper H.,
MukuddemPetersen J.,
Petersen M. A.
Publication year - 2005
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.609
Subject(s) - capital adequacy ratio , capital requirement , risk adjusted return on capital , risk weighted asset , basel ii , basel iii , actuarial science , economic capital , economics , basel i , capital (architecture) , business , econometrics , financial capital , capital formation , microeconomics , profit (economics) , archaeology , history
Regulation related to capital requirements is an important issue in the banking sector. In this regard, one of the indices used to measure how susceptible a bank is to failure, is the capital adequacy ratio (CAR). We consider two types of such ratios, viz. non‐risk‐based (NRBCARs) and risk‐based (RBCARs) CARs. According to the US Federal Deposit Insurance Corporation (FDIC), we can further categorize NRBCARs into leverage and equity capital ratios and RBCARs into Basel II and Tier 1 ratios. In general, these indices are calculated by dividing a measure of bank capital by an indicator of the level of bank risk. Our primary objective is to construct continuous‐time stochastic models for the dynamics of each of the aforementioned ratios with the main achievement being the modelling of the Basel II capital adequacy ratio (Basel II CAR). This ratio is obtained by dividing the bank's eligible regulatory capital (ERC) by its risk‐weighted assets (RWAs) from credit, market and operational risk. Mainly, our discussions conform to the qualitative and quantitative standards prescribed by the Basel II Capital Accord. Also, we find that our models are consistent with data from FDIC‐insured institutions. Finally, we demonstrate how our main results may be applied in the banking sector. Copyright © 2005 John Wiley & Sons, Ltd.