Non-maturity deposits are a major source of funds for traditional banks. The deposit valuation model described by Jarrow and van Deventer (1998) assumes a short-term liquidity option and a single remuneration rate. We extend the traditional valuation model to the case where, as in the Benelux, the deposits are remunerated first on the current balance (at the base rate) and where an additional premium rewards the deposits that have remained on the account for a certain period (at the fidelity premium rate). We show the existence of an additional term in the valuation formula, the premium complement, allowing the total remuneration rate to be higher than the short-term interest rate and still yield positive net present value. The premium complement depends positively on the base deposit spread during the holding period and negatively on the proportion of stable deposits. Hence, the model explains why a rational bank may offer a fidelity premium higher than the deposit spread. The 11-year data provided by a European regional bank are used to empirically compare the valuation models. The results show that the proportion of stable deposits plays an important role in the valuation and must be taken into account accurately. The effect of changes in the remuneration policy on the optimal proportion of stable deposits is also analysed.
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