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A multiperiod model for estimating the cost of deposit insurance under the Basel III minimum capital requirement
Author(s) -
Muller Grant E.
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6248
Subject(s) - capital requirement , capital adequacy ratio , risk weighted asset , basel iii , economics , risk adjusted return on capital , portfolio , minimum capital , econometrics , basel ii , cost of capital , interest rate , microeconomics , monetary economics , financial economics , capital formation , financial capital , profit (economics) , incentive
Under the Basel III regime, a commercial bank is considered adequately capitalized if it maintains a ratio of capital to total risk‐weighted assets or capital adequacy ratio (CAR) of at least 8%. We model a commercial bank that complies with Basel III's minimum capital requirement on an interval [ 0 , T ] for T > 0 . The bank model is achieved via a specific rate of capital influx that fixes the bank's CAR at the minimum prescribed level of 8%. On the basis of this capital influx rate, we derive models for the bank's asset portfolio and capital dynamics required for maintaining the CAR at the minimum prescribed level. For the aforementioned bank, we further study a deposit insurance (DI) pricing problem with a coverage horizon equal to T years. More specifically, we employ a multiperiod DI pricing model to approximate the cost of DI for the bank on the interval [ 0 , T ] , where the constant (minimum) CAR is maintained. We study the behaviours of the models leading to the constant (minimum) CAR, and the behaviour of the DI premium estimate by means of numerical simulations. In the simulation study pertaining to the DI premium estimate specifically, we determine the effects of changes in the bank's initial leverage level (deposit‐to‐asset ratio), the DI coverage horizon, and the volatility of the asset portfolio on the DI premium estimate.