Mind the Solvency II Gap: A Coherent Measure of Market Consistent Embedded Value to Interest Rate Risk in ALM

Abstract

This paper derives Asset and Liability Management ('ALM') interest rate risk measures (i.e. duration and convexity gaps) applicable to Life insurance companies that are adequate such as asset and liability-driven strategies can be used within a mix of tactics and instruments to achieve financial objectives, for a given set of ALM interest rate risk indicator tolerances. The approach adopted relies on a half-way approach between immunization (i.e. duration match) and dedication (i.e. cash flows match) that consists to match both the duration and convexity of the market value of assets and best estimate liabilities as well as the inclusion of partial and key-rate duration and convexity matches. The recent changes in regulation through the adoption of a market consistent framework (i.e. MCEV) combined to distressed economic conditions with failing equity markets, brutal changes in interest rates and spreads further increase the motivation for a rigorous and coherent definition of ALM risk measures in order to manage appropriately interest rate risk of Life insurance companies. Through this paper, effective and key-rate duration (and convexity) gaps are derived based on the interpretation of ALM risk indicators as approximation of interest rate sensitivities within a market consistent framework. Those concepts are discussed with respect to their usefulness for ALM of Life insurance companies. This paper is of high interest in the context of Solvency II given the lack of guidelines provided by EIOPA regarding the treatment and management of interest rate risk from an ALM perspective.

Keywords: asset and liability management (ALM), interest rate risk, market consistent embedded value (MCEV), duration, convexity, duration gap, convexity gap, key-rate duration, key-rate convexity, immunization, dedication, half-way approach, target duration, convexity impact, stochastic ALM, DFA

JEL Classification: G00, G11, G12, G20, G22, G28