JOURNAL ANALYSIS

Theme
Demand Deposit
Title
Hedging Interest Rate Margins on Demand Deposits

Author
Mohamed Houkari, Jean-Paul Laurent ;
Université de Lyon, Université Lyon 1, ISFA Actuarial School, and BNP Paribas Financial
Models Team

Year
2010

INTRODUCTION
Under IFRS – the new 2005 international accounting standards – banks account demand deposits at amortized cost. Moreover, the US Securities and Exchange Commission asks American banks to report in annual (10-K) and quarterly (10-Q) documents, indicators concerning interest rate margins and their sensibilities to interest rate shocks. However, in internal processes, many banking establishments perform the computation of full fair-value indicators for the market value of equity. As for demand deposits, the well-known fair-value approach developed for example in Hutchison and Pennacchi (1996) and Jarrow and van Deventer (1998) has been the main way to assess demand deposits so far.

PROBLEM
A worldwide study of the Bank for International Settlements shows that risk mitigation in interest rate margins has been a significant concern for banks during these last twenty years.
PURPOSE
Show how interest rate margins have become a major point of concern for banking establishments today, with a focus on the US case. Propose a modeling framework for demand deposits, interest rates and the interest rate margin.

RESEARCH METHODOLOGY
With Modeling Framework

Market Rates
We consider some time horizon T such that we deal with the corresponding quarterly interest rate margin. Besides, we assume that the forward Libor rate at horizon date T for the time period δT > 0 of the interest rate margin follows a Libor Market Model, as defined in Brace, Gatarek and Musiela (1997) and Miltersen, Sandmann and Sondermann (1997): dL L ( dt dW (t)) t t L L L = μ +σ , (1)

Demand Deposit Amount
We assume that the demand deposit amount follows:
dK K ( dt dW (t)) t t K K K = μ +σ (2)
where K W is a standard Brownian motion. For simplicity, the trend K μ and the volatility K σ
The correlation between the variations of demand deposit amount and that of interest rates can be related to money transfers between deposit accounts and other types of deposits.
We refer to the Engle and Granger method detailed in Ericsson and MacKinnon (1999) to estimate the correlation parameter between the deposit amount and the market rate. Janosi et
al. (1999) use a very similar method, although they also pay attention to autocorrelation and short term effects.

RESULTS AND ANALYSIS
The negative values for the ES and the VaR in the upper line are due to the fact that the margin at final date is mostly positive16. Thus, the VaR at 99.95% of the interest rate margin is (-1.90) for an initial deposit amount of 100. We see, in Table 5.6a above, that using the optimal dynamic hedging strategy makes the risk decrease by 0.39 to (-2.29), thus constituting a better risk reduction than other strategies, in this VaR framework. The same actually holds for the ES and the standard deviation.

In general, the risk reduction implied by the optimal dynamic strategy is almost always more significant: even when there is no customer rate, it goes to 0.45 in ES and 0.46 in VaR. This shows some robustness of the optimal dynamic strategy also with respect to the choice of the risk criterion. Moreover, this somehow makes us confident with the meanvariance optimization framework, more tractable than some mean-VaR or mean-ES framework.

CONCLUTIONS
In this article we dealt with the mitigation of the risk contained in interest rate margins. We assume the demand deposit amount to carry some source of risk called ‘business risk’, orthogonal to market risk. Thus, we compared these dynamic strategies with some static strategies. We show that identifying the interest rate-related optionality in interest rate margins is a quite satisfactory alternative to dynamic hedging strategies. Moreover, both this method and the use of dynamic strategies lead to quite robust results, with respect to the margin’s profile specification.
However, the use of dynamic strategies also better deals with the specific risk embedded in demand deposits. Moreover, we show that they also exhibit some robustness with respect to the risk criterion. This is a positive conclusion for the use of mean-variance optimization and the related dynamic hedging strategies, since they display good results with respect to other risk measures.