An Equilibrium Model of Interbank Networks Based on Variational Inequalities

Table 1

Notations for the equilibrium model.

Notations	Description
𝑀	The number of banks in the interbank market
𝑁𝑡	Trust network in the interbank market
𝑁𝑐	Credit network in the interbank market
𝑖	A bank with liquidity surplus, 𝑖=1,…,𝑀0
𝑗	A bank with liquidity shortage, 𝑗=1,…,𝑀−𝑀0
ℎ𝑖𝑗	The trust level of bank 𝑖 to bank 𝑗, 0≤ℎ𝑖𝑗≤1
𝑣𝑖𝑗	The value of the trust level ℎ𝑖𝑗 for bank 𝑗, 𝑣𝑖𝑗(ℎ𝑖𝑗)=𝑎𝑖𝑗ℎ𝑖𝑗+𝑐𝑖𝑗, 𝑎𝑖𝑗 and 𝑐𝑖𝑗 are constants, 𝑎𝑖𝑗>0
𝑆𝑖	The scale of liquidity surplus of bank 𝑖
𝐷𝑗	The scale of liquidity shortage of bank 𝑗
𝑞𝑖𝑗	The scale of credit lending of bank 𝑗 from bank 𝑖
𝑙𝑖	The lending rate of bank 𝑖
𝑏𝑗	The borrowing rate of bank 𝑗
𝑝𝑖𝑗	The interest rate for the credit lending 𝑞𝑖𝑗, 𝑝𝑖𝑗=𝑝𝑖𝑗(𝑙𝑖,𝑏𝑗)
𝑏𝑖𝑗	The opportunity cost of bank 𝑖 for the credit lending 𝑞𝑖𝑗, 𝑏𝑖𝑗=𝑏𝑖𝑗(𝑞𝑖𝑗)
𝑟𝑖𝑗	The risk faced by bank 𝑖 for the credit lending 𝑞𝑖𝑗, 𝑟𝑖𝑗=𝑟𝑖𝑗(𝑞𝑖𝑗,ℎ𝑖𝑗,𝑝𝑖𝑗)
𝑓𝑖𝑗	The borrowing cost of bank 𝑗 for the credit lending 𝑞𝑖𝑗, 𝑓𝑖𝑗=𝑓𝑖𝑗(𝑞𝑖𝑗,ℎ𝑖𝑗,𝑝𝑖𝑗)