Firm value, illiquidity risk and liquidity insurance

Our interest here concerns liquidity supply to firms. We first examine the relation between firm value and access to liquidity supply, and then we investigate the existence conditions and efficiency properties of financial contracts with a liquidity covenant in a continuous-time, infinite-horizon stochastic model of a repeated firm-investors relationship where the key problem is the mutual commitment between the two parties. To model this problem we consider liquidity supply as a stochastic “regulator mechanism” that prevents the firm's ability to pay from falling below a predefined threshold (here the market fixed coupon), and we then apply recent developments in dynamic programming techniques for “regulated processes” to obtain a close form solution for the firm's value. Our main finding is that efficient, i.e. actuarially fair and renegotiation-proof contracts emerge in the absence of perfect commitment as the firm and the investor can exert mutual threat of termination.