Interest Rate Risk in the Banking Book: A Closed-Form Solution for Non-Maturity Deposits

Abstract

I present an analytical valuation framework for the management of fixed-income instruments traded in imperfectly competitive markets, like demand deposits and credit card loans in the banking book, inter alia, to stabilize the abnormal profit margin. Banking book instruments contain embedded options such as withdrawal rights, discretionary pricing, rate clustering and zero-based floors. Analytical solutions speed up computation time to calculate valuations, earnings and risk measures like closed-form expressions for margin spreads, hedge ratios and parameter sensitivities. Asymptotically, according to martingale central limit theorems and thanks to the long-term nature of the banking book, Gaussian approximations can be applied.

Keywords: Basel Committee on Banking Supervision (BCBS), Asset and Liability Management (ALM), Fourier-Stieltjes Transform Analysis, Martingale Central Limit Theorem, Zero Lower Bound

JEL Classification: E43, G11, G21