Integrating macroeconomic variables into behavioral models for interest rate risk measurement in the banking book

Zhongfang He

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This paper provides an approach to integrate macroeconomic variables into behavior models for measuring the interest rate risk (IRR) of the banking book such that projections of macroeconomic variables are consistent with prescribed IRR interest rate scenarios.
Each macroeconomic variable is decomposed into an interest-rate-correlated component and a macro-specific component that is uncorrelated with interest rates. In measuring interest rate risks, scenarios of the yield curve are fed into the interest-rate-correlated component of the macroeconomic variable to generate its projections, while the macro-specific component, being uncorrelated with interest rates, is specified as a constant (e.g. historical average or tail percentile). The sum of the two components results in projections of the macroeconomic variable that are consistent with the IRR interest rate scenarios.
The decomposition of the macroeconomic variable is performed through the nonparametric kernel ridge regression that extracts the expectation of the macroeconomic variable conditional on interest rates.
Implementation of the proposed approach in practice is straightforward as the final estimate is of a linear functional form and has a closed-form solution.

Abstract

Recent Basel Committee on Banking Supervision standards on interest rate risk in the banking book require the consideration of macroeconomic variables for modeling client behaviors, while no macroeconomic risk scenarios are prescribed by regulators or are generally agreed in the industry. Since macroeconomic variables and interest rates are correlated, projecting macroeconomic variables for interest rate risk measurement poses the challenge of maintaining consistency with regulator-prescribed interest rate scenarios. This paper proposes an approach to integrate macroeconomic variables with interest rate scenarios. The conditional expectation of macroeconomic variables on interest rate variables is used to capture their interdependence. Based on the mathematical properties of conditional expectation, we derive its nonparametric estimator. The resulting projections of macroeconomic variables are fully consistent with the given interest rate scenarios and are convenient for implementation in practice. An empirical application to Canadian fixed-term deposits is conducted to illustrate the proposed approach.

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