Under the Basel II Accord, banks and other Authorized Deposit-taking Institutions
(ADIs) have to communicate their daily risk estimates to the monetary authorities
at the beginning of the trading day, using a variety of Value-at-Risk (VaR) models
to measure risk. Sometimes the risk estimates communicated using these models
are too high, thereby leading to large capital requirements and high capital costs.
At other times, the risk estimates are too low, leading to excessive violations, so
that realised losses are above the estimated risk. In this paper we analyze the profit
maximizing problem of an ADI subject to capital requirements under the Basel II
Accord as ADI's have to choose an optimal VaR reporting strategy that minimizes
daily capital charges. Accordingly, we suggest a dynamic communication and
forecasting strategy that responds to violations in a discrete and instantaneous
manner, while adapting more slowly in periods of no violations. We apply the
proposed strategy to Standard&Poor's 500 Index and show there can be
substantial savings in daily capital charges, while restricting the number of
violations to within the Basel II penalty limits. |