A model of equilibrium in markets of cash balances

A model is presented to characterize the equilibrium in markets of short‐term loans. First, the cash demand is characterized as the optimal balance maintained to avoid the losses produced by some portfolio with random payoffs. This problem is formulated in actuarial terms in such a way that the optimal balance is expressed as the quantile function of the probability distribution describing the underlying risk (i.e. the value‐at‐risk). An expression is then obtained for the semi‐elasticity of the demand for balances with respect to the interest rate. The effects of credit and investment flows over the equilibrium can be precisely described on these grounds. In the particular case, when the series of price returns of the underlying portfolio is described by a Gaussian probability distribution, episodes of liquidity crises can be corresponded to specific combinations of the risk parameters and the level of the interest rate. Theoretical evidence is thus given of these phenomena.