Stochastic Controllability of Linear Interest Rate Models

Petersen, Mark A.; Raubenheimer, Helgard; Walt, Frederik C. van der; Rooy, H.F. Van

doi:10.1007/978-3-0348-7881-4_21

Cited by 2 publications

(2 citation statements)

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“…We assume that our bank invests in a market with n þ 1 financial assets. In our contribution, the risk-free rate of interest is modelled as a one-factor diffusion process (see, for instance, Reference [35] …”

Section: Bank Assetsmentioning

confidence: 99%

“…In our paper, we consider equity and leverage CARs (collectively known as NRBCARs; defining formulae given by (24) in Section 3.2) and Basel II and Tier 1 CARs (together classified as RBCARs; defining formulae given by (35) in Section 4.4) as identified by the FDIC (see, for instance, Reference [13]). The definitions of these CARs are provided in ensuing discussions (Figure 1), while Figures 2 and 3 highlight and explain differences between them.…”

Section: Introductionmentioning

confidence: 99%

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Continuous‐time stochastic modelling of capital adequacy ratios for banks

Fouche

Mukuddem‐Petersen

Petersen

2005

Appl Stoch Models Bus & Ind

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SUMMARYRegulation 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 riskweighted 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.

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Section: Bank Assetsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%