A Stochastic Approach to the Measurement of Interest Rate Risk in the Banking Book

Abstract

Interest rate risk of a financial position is the potential loss in value arising from adverse movements of the interest rate term structure. Banks calculate rough measures of interest rate risk in their banking book (IRRBB) as imbalance between changes in value of their financial assets and liabilities in response to hypothetical shocks of default-free interest rate curve. This method leaves unresolved at least two fundamental issues. Firstly, yield curve shocks defined by regulators and applied as standard scenarios by all banks remain largely judgmental; this induces scarce reliability on interest rate risk measures, generally calculated for regulatory compliance purposes and broadly unused in risk management practices. Secondly, the most common systems for asset and liability management (ALM) neglect the fact that the fair value of credit risky financial instruments reacts not only in response to interest rate shocks, but it is also sensitive to credit spread fluctuations. For decades, an improbable parallel raise of default-free interest rate curve has been considered as a standard scenario in almost all systems for ALM. Though this assumption is commonly deemed unrealistic and objectively incapable to deliver a meaningful appraisal of IRRBB, it has been widely used for the sole purpose of giving monetary dimension to the duration-gap between assets and liabilities that ended up being the unique determinant of IRRBB measure. In recent years, with the objective to increase the consistency of interest rate risk measures and inform decision processes inside banks in a correct manner, regulators and practitioners expanded the range of simulated interest rate shocks by including negative shocks and non-parallel shifts of the interest rate curve. Nevertheless, these solutions must be considered largely misleading since a whatever interest rate scenario always results from a discretionary decision of supervisors or banks. Past experience suggests that deterministic approaches, although based on some mathematical method, inevitably result in unreliable potential loss estimates and large fluctuations of IRRBB measures over time. In this article, we explore the possibility of using Monte Carlo simulation in order to identify firm specific adverse interest rate shocks and define the frequency distribution of delta values of the banking book. The generation of a wide range of interest rate shocks, combined with common techniques for ALM, produces consistent measures of IRRBB. A multivariate stochastic process, compliant with option pricing theories, is completely fed by market data.