The funds market bank problem

TL;DR

This paper models a bank's optimal funds trading strategy in a stochastic environment with different discount rates, deriving explicit thresholds for buying and selling to meet reserve requirements efficiently.

Contribution

It introduces an explicit optimal control strategy for a bank trading in the funds market with asymmetric discount rates and stochastic reserve demands.

Findings

Optimal thresholds for buying and selling funds are explicitly derived.

The model accounts for different discount rates for purchases and sales.

The strategy minimizes costs while maintaining reserve requirements.

Abstract

This paper considers the problem faced by a bank which trades in the funds market so as to maintain the reserve requirements and minimize the costs of doing that. We work in a stochastic paradigm and the reserve requirements are determined by the demand deposit process, modelled as a geometric Brownian motion. The discount rates for the cumulative funds purchased and the cumulative funds sold are assumed to be different. The optimal strategy of the bank is explicitly found and it has the following structure: when bank reserves lower to an exogenously threshold level the bank has to purchase funds; when bank reserves tops an endogenously threshold level the bank has to sell funds