On the risk management of demand deposits: quadratic hedging of interest rate margins

This paper examines the problem of hedging banks interest rate margins. We assume that the demand's deposits follow an exponential Levy process with potential jumps. The forward market rates are assumed to follow the standard market model introduced by Brace et al. (Math Finance 7(2):127-155, 1997). As Adam et al. (Hedging interest rate margins on demand deposits, Universite Paris 1 Pantheon-Sorbonne working paper, 2012), we consider that deposit rates depend linearly on market rates. Face to incompleteness, the liability manager must hedge both interest rate and demand deposit risks. For this purpose, we introduce various quadratic hedging criteria, allowing us to provide explicit hedging strategies that we further analyze. We illustrate in particular the impact of both the trends and the volatilities of interest rates and demand deposits.