We use a two-stage option-based model to study how Asymmetric information, capital requirements, loan commitment rate and the optimal loan rate relate to one another under an uncertain loan loss source. This model shows that there will be synergies between lending and deposit-taking to the extent that both require the bank to hold large liquid asset balances if its term loans and loan commitments are substitutes. Otherwise, narrow banking management is required by the bank. However, if the bank's term loans and loan commitments are substitutes (complements) and the bank conducts strategic substitutes (strategic complements), there is also real narrow banking. Our findings provide an alternative explanation for the synergy or narrow banking management, which answer the question: if there is real synergy (narrow banking), a forced switch to narrow banking (synergy) could lead to a large inefficiency.
Journal of Information & Optimization Sciences 26(1), pp.143-163