1.Calculating the General Market risk charge

Calculate the general market risk capital charge for XYZ bank’s interest rate positions using the maturity method.

Long position in a qualifying bond: Market value AED 13.33m. Residual maturity 8 years & coupon 8%

Long position in a government bond: Market value AED 75m. Residual maturity 2 months & coupon 7%

Interest rate swap: Notional value AED 150m. Residual life of swap 8 years & bank receives floating rate interest and pays fixed. Next interest fixing after 9 months

Long position in interest rate government bond future: Contract size AED 50mn.

The treatment of interest rate future positions assume a bank is exposed to a long position in a 6-month interest rate future bought today and settled in two months' time. The long position in interest rates needs to be slotted into the 6-12 months’ time band because the maturity of the long position is considered to be eight months. This is because the position is taken on today and will be settled in two months with a maturity of six months.

Delivery date after 6 months & remaining maturity of the CTD government security 3.5 years.

Cheapest to deliver CTD refers to the underlying instrument that result in the greatest profit or the least loss when delivered in satisfaction of futures contracts.

Calculating the general market risk capital charge comprises two main steps and a number of sub-steps.

Step 1: Map each interest rate position

We are using the maturity method to map the positions. None of the bank’s positions have a coupon of less than 3%, so we will use a ladder of 13 time bands. Each position is mapped to the appropriate time band according to its residual maturity.

Step 2: calculate the total capital charge

Overall net open position

The net open position is the sum of all the positions across all the time bands. The net open position is AED 3m short, which leads to a capital charge at 100% of AED 3,000,000.

Calculation:

+75*0.2%=+0.15

-50*0.4%=-0.2

+150*0.7%=+1.05

+50*2.25%=+1.125

-150*3.75%=-5.625

+13.33*3.75%=+0.5

Vertical disallowance

The long position of AED 0.5m is offset against the short position of AED 5.625m as per the marked area. The matched position is AED 0.5m and the net open position is AED -5.125m.

This leads to a capital charge of 10% of AED 0.5m, or AED 50,000

Calculation

Matched position = 0.5

Net open position = -5.625+0.5= -5.125

Horizontal disallowance

The third part of the capital charge is a charge for the horizontal disallowance. There are three rounds of horizontal offsetting.

In round 1, the horizontal disallowance within each zone is calculated. In this example, charge applies to zone 1 only because it is the only zone with a long and a short position. (With more than one position). The short position, -0.2 is offset against the total long position, +1.2. The matched position is 0.2 and the net open position is +1.

The capital charge for the horizontal disallowance within zone 1 is 40% of AED 0.2m, or AED 80,000

In round 2, calculate the horizontal disallowance between adjacent zones, i.e., between:

Zone 1 and zone 2

Zone 2 and zone 3

In this example, zone 1 and zone 2 both contain long positions, so there is no matched position and therefore no offsetting between these zones. The long position of 1.125 in zone 2 is offset against the short position of -5.125 in zone 3. The matched position is 1.125 and the net open position is -4. The capital charge for the horizontal disallowance between zones 2 and 3 is 40% of AED 1.125m= AED 450,000.

In round 3, we calculate the horizontal disallowance between zones 1 and 3.

In this example, the long position of 1 in zone 1 is offset against the short position of -4 in zone 3. The matched position is 1 and the net open position is -3. The capital charge for the horizontal disallowance between zones 1 and 3 is 100% of AED 1m = AED 1m.

After the three rounds of horizontal offsetting, the total charge for the horizontal disallowance is AED 80,000 + AED 450,000 + AED 1,000,000 = AED 1,530,000

Having completed the horizontal and vertical offsetting, the remaining overall net open position is AED 3m, which is equivalent to the overall net open position we calculated across all time bands when we calculated the first part of the capital charge.

We have now calculated the total capital charge for general market risk for this example.

   2.Specific Market Risk – Example

Relate to the same example as above.

Given that, the government bonds are AAA-rated and that the qualifying bond is BBB-rated.

The interest rate swap does not incur a specific risk charge. The AAA-rate government bonds incur a 0% specific risk charge. The qualifying bond has a residual maturity of 8 years and is BBB-rated, so if has a specific risk charge of 1.6%

The capital charge is 1.6% of AED 13.33m, or AED 213,280.