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# THE GAP MODEL

Interest rate gaps are very popular because they measure the sensitivity of the net interest income (N11) to a shift of rates. At this stage it is convenient to assume that all rates unknown as of today move by the same amount (parallel shift).

When the variable rate gap (interest rate sensitive assets minus interest rate sensitive liabilities) is positive, the volume of assets that is interest rate sensitive is larger than the volume of liabilities that are rate sensitive. If the index is common to both assets and liabilities, the N11 increases with interest rates, and conversely when the variable rate gap is negative. When the variable rate gap is zero, the N11 is insensitive to changes in interest rates. It is said to be "immune" to variations of rates. The variable rate gap is the sensitivity of N11 to a shift of interest rates. The notations are:

• N11 net interest income

• IRSA and IRSL are interest rate sensitive assets and liabilities

• / — interest rate.

The change of net interest income (N11) due to the change in interest rate Ai is:

ANIT= (IRSA-IRSL)Az

Assume that the variable rate gap is +200. The variation of the N11 in the above example is 2 when the rate changes by 1% or 100 x 1%. The basic formula relating the variable rate gap to net interest income is:

ANII = (IRSA - IRSL)A/ = (interest rate gap)Az

The above formula is only an approximation. Several adjustments are required for improving the accuracy of the gap model.

Using a global gap assumes that there is a single reference, and, notably, a parallel shift of all rates. Regulations impose testing the effect of parallel shifts on N11, using shifts of 1% or 2%. However, since there are several interest rate references, there are as many variable rate gaps as there are references. Breaking down the variable rate gap into gaps by interest rate reference provides the sensitivities of N11 to these references, for example rates applying to different maturities.

A gap is calculated over time bands, for example a month. The change of interest accrued modeled with the gap assumes that the reset date occurs at the beginning of the time band. If the reset date is close to end of month, the change of interest revenue or cost would be overestimated. The correct change of N11 depends on any concentration of reset dates other than beginning of month. The appendix shows the exact calculation of the N11 when the interest rate gap is zero but reset dates differ: the N11 remains sensitive to a change of interest rates in spite of the zero gap.

The gap nets values of assets and liabilities. Over a month, these amounts change. A gap derived from values as of the beginning of the month would assume that such changes do not occur. A common practice is to use values of assets and liabilities that are averages of daily values over the month for smoothing out within-period variations.

The gap model is very popular because it is very simple and because it measures the sensitivity of the N11 to the interest rate movements. Hedging the interest rate risk of the N11 becomes very simple since it implies changing the gap, which can be achieved with hedging instruments such as interest rate swaps or forward contracts. Found a mistake? Please highlight the word and press Shift + Enter Subjects