Pricing of Loan Commitments for Facilitating Stochastic Liquidity Needs

A bank loan commitment is often priced as a European-style put option that is used by a company with a known borrowing need on a known future date to lock in an interest rate. The literature has abstracted some of the important institutional features of a loan commitment contract. First, the timing, number, and size of the loan takedowns under such a contract are often random, rather than fixed. Second, companies often use loan commitment contracts to reduce the transaction costs of frequent borrowing and to serve as a guarantee for large and immediate random liquidity needs. Third, commercial banks maintain liquidity reserves for making random spot loans or random committed loans. Partial loan takedowns raise, rather than lower, the opportunity cost of a committed bank’s holding of excess capacity. This paper introduces a “stochastic needs-based” pricing model that incorporates these features. Simulations are conducted to illustrate the effects of various parameters on the fair price of a loan commitment.