Hedging Strategies for Net Interest Income and Economic Values of Equity

The changes in Interest rate risk in the banking book ( IRRBB ) of Basel capital frameworks Pillar 2, where the regulator prescribed a set of stress scenarios and shocks to a standardized interest rate risk measures on changes of Economic Value of Equity (EVE) and Net Income Interest (NII) force banks to model interest rate risks and develop hedging strategies to mitigate the sensitivity to interest rate shocks.In this work we define, model and compute both the NII and the EVE indicators. We study early renegotiation models, based either on an optimal exercise or a statistical model. Finally, we discuss hedging strategies for the NII and the EVE based on both variance and sensitivities minimization. The framework is flexible enough to take into account a wide variety of operational situations, including regulatory ones. To test it, we analyze numerically hedging strategies aiming to reduce the sensitivity of ALM risk measures. Notably, we show that the NII and the EVE are opposite measures: lowering the sensitivity of one of this measures increases the sensitivity of the other. However, anticipated refunds and renegociation effects might temper this conclusion.To reach these goals, we shift from a classical scenario-based definition of the NII and the EVE to a stochastic one, that is quite similar to a Front-Office portfolio analysis. However, there is a drawback in this approach: the targeted applications require not only to compute the EVE and the NII indicators, but also all their conditional futures prices and sensitivities' values. In an operational context, where the number of risk sources can be large, classical numerical methods face the so-called curse of dimensionality problem.To tackle this difficulty, we conduct our numerical experiments using a financial mathematics framework, embedding a partial differential equations (PDE's) solver, that overcomes the curse of dimensionality