# Lines without Maturity

As with liquidity gaps, interest rate gaps require maturities. With all lines without maturity, the best proxy that we can have is using effective maturity when it differs from a contractual maturity or when there is no maturity at all. Conventions might help, such as for demand deposits, but do not resolve the issue. Multiple business scenarios are required and they require simulations rather than gap models.

# Mapping Interest Rates to Selected Risk Factors

It is difficult to deal with all interest rates serving as references for assets and liabilities. Banks select specific vertices along the yield curve, or risk factors. All rates that do not match those selected reference rates are correlated with them, but not perfectly. The usage of a small number of selected interest rates requires mapping all balance sheet items to those. The process creates basis risk, or the residual risk due to differences between selected and actual rates. One solution is to relate actual rates, by product segment, to the selected reference rates and to use sensitivities for calculating "standardized gaps."

Statistical techniques provide the sensitivities. The average rate of return of a sub-portfolio, for a product family for instance, is the ratio of interest revenues (or costs) to the total outstanding balance. It is feasible to construct times series of such average rates over as many periods as necessary. A statistical fit to observed data provides the relationship between the average rate of the portfolio and the selected rates. A linear relation is such as:

The coefficient Pj is the sensitivity of the loan portfolio rate with respect to the index r The residual e is the random deviation between actual data and the fitted model. A variation of the market index of 1% generates a variation of the rate of the loan portfolio of *$l* x 1%. It captures the basis risk, except for the residual error.

A standardized gap weights the assets and liabilities by their sensitivities to the selected reference rates. For example, if the return of a segment of loans has a sensitivity of 0.8 with respect to the short-term market rate, it will be weighted with 0.8 in the gap calculation.

The alternate solution is to use directly the reference rates of contracts at the level of individual transactions. Vendors' software dedicated to asset liability management provides the capability of calculating exact reset dates with multiple reference rates, as long as banks have the information.