Operational risk capital and insurance in emerging markets

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The aggregated loss S combines two random variables ( n and zi) whoseconditional distributions are previously estimated. Therefore the aggregation Sis itself a random variable whose distribution has to be determined by convolutionmethods.The frequency of loss events ( n ) has an estimated probability distributiondenoted by pn= Pr( N = n)while the loss severity distribution ( z ) hasestimated density distribution and cumulative distribution functions denoted byf z y F z , respectively. According to Bee (2005) the cumulative probability distributionfunction of S is defined as:Where pn=Pr(N=n) and Pr(w£SI N = n ) is the probability tohave a cumulative loss lower than S given that n events have occurred.Due to the fact that S is the cumulative sum of loss severities, its distributionfunctions can be estimated by the convolution procedure outlined in AppendixA. Once this is done, expected losses as well as risk metrics can be extracted.In particular, operational risk capital is such that it covers the unexpected lossesfor the period capital reserve was made. Unexpected losses are defined as thedifference between a high percentile of the loss distribution (According to Basel 2,99,9-percentile) and the expected loss value.It is important to highlight that the estimation of tail percentiles is always uncertainbecause it depends on the specific form of loss distribution and the type of dataunder consideration. Therefore operational capital estimation must account for thisuncertainty in the form of operational capital intervals.III.1.2 OPERATIONAL RISK CAPITAL UNDER THE PRESENCE OF INSURANCEIntroduction of insurance requires first the consideration of qualitative guidelinesestablished by the BCBS, as well as the inclusion of particular insurance contractfeatures.Insurance contracts change the form of the original loss distribution ( ) FSbecause net losses with insurance are lower than those obtained in the absenceSBS Revista de Temas Financieros 38
of insurance. Following Insurance Companies (2001), the standard elements ofinsurance can be summarized in Table 1.Table 1: Quantitative conditions of the insurance contractParametersd eeD al eeL aDefinitionSpecific deductible to each loss eventAggregate deductibleLimit for each event of lossAggregate limitCR p E(0,1) Credit risk haircut of the insurer 18The interpretation of these variables is as follows:• If a loss event of size zioccurs, the loss payment by the insurer is: z _ i d ee . Thispayment can not be higher than the limit l ee.• If there are n loss events in the insurance period, the total sum of amountsthat the insurer pays must be higher than the aggregate deductible Dabutlower than the aggregate limit. La. When this occurs the insurer pays out anamount in excess of Da. Otherwise, the loss payment is equal to the maximumcoverage L .a• This means that cumulative high losses are effectively insured while the smallcumulative losses are absorbed by the insured bank.• The insurance effect under the features of the contract outlined above is thenobtained using the following formula:• According to these equations, cumulative losses ( S ) with insurance are lowersegthan those in the absence of insurance ( S ). Therefore, the loss distributionfunction shifts to the left as described in Figure 1. This insurance contract allowsthe 99-percentile to reduce more than the expected loss value and so lowersoperational risk capital.18 Even though the BSCB establishes a minimum rating of A for insurance providers, the paper considers lower-rated insurers not reaching vulnerable levels. Thisis because it is too stringent to require emerging-market financial institutions to operate with insurers that rank better than their own countries. For this reason, itis necessary to perform an adjustment according to the paying ability rating of the insurance company.SBS Revista de Temas Financieros 39
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Page 8: models is that there are no referen
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Page 15 and 16: A straightforward way to model the
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Page 21 and 22: V. REFERENCES1. Bee, Marco; “On M
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