This paper investigates the implications of the uncertain timing and usage of loan commitments for the optimal level of bank capital. We use trended Brownian motion to proxy the stochastic takedown of credit lines. Relying on “time to first passage” mathematics, we derive a probability density function for the time to depletion of the bank credit line as well as the likelihood for the time to exhausting the sources of liquidity that fund the loan takedown. Armed with these analytical results, we solve for the optimal level of bank capital within a simultaneous equation framework in order to capture the interrelationships of the endogenous variables. The optimality conditions produce a system of integral differential equations which refuse to yield reduced form solutions and provide no immediate intuition. Therefore, the maximizing values of the bank’s decision variables were simulated over a host of realistic scenarios. We document the comparative static behavior of the bank’s decision variables when equity is unencumbered by capital requirements and, also, examine the impact of the same parametric changes on bank behavior when equity is a fixed proportion of lending. Further simulations produce the expected time to liquidity depletion under different capital requirement schemes.
Review of Quantitative Finance and Accounting – Springer Journals
Published: Nov 20, 2014
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera