A Model of Network Formation for the Overnight Interbank Market A Model of Network Formation for the Overnight Interbank Market Mikhail Anufriev a Andrea Deghi b Valentyn Panchenko c Paolo Pin d a University of Technology Sydney b Università degli Studi di Siena c University of New South Wales, Sydney d Università Bocconi seminar at Bocconi University, Milan 16 October 2017 1 / 57
A Model of Network Formation for the Overnight Interbank Market Outline Introduction 1 Interbank Market Model 2 Variables and payoffs Solution Equilibrium Network Configurations Interest Rate Discussion and Extensions 3 Empirics of Interbank Networks Core-Periphery Structure Policy Implications Systemic Risk and Network Approach Conclusion 4 2 / 57
A Model of Network Formation for the Overnight Interbank Market Introduction Plan Introduction 1 Interbank Market Model 2 Variables and payoffs Solution Equilibrium Network Configurations Interest Rate Discussion and Extensions 3 Empirics of Interbank Networks Core-Periphery Structure Policy Implications Systemic Risk and Network Approach Conclusion 4 3 / 57
A Model of Network Formation for the Overnight Interbank Market Introduction Interbank Market Overnight interbank market unsecured interbank loans to balance short-term liquidity typically over one night bilateral agreements seting quantity and interest rate over-the-counter (for US Fed funds) or transparently centrally organized (e.g., e-MID) directly related to Monetary Policy and financial stability helps banks to manage their reserves, offset liquidity shocks CBs target prevalent interbank rate freeze of IB market during GFC negatively impacted financial system reveals information about what banks expect about credibility of other banks and overall market conditions 4 / 57
A Model of Network Formation for the Overnight Interbank Market Introduction Interbank Market e-MID: electronic Market for Interbank Deposit 5 / 57
A Model of Network Formation for the Overnight Interbank Market Introduction Interbank Market Theoretical Literature of Overnight Markets Poole (JF, 1968) corridor systems with reserve requirements banks are uncertain about their reserves Afonso and Lagos (ECTA, 2015) banks meet at random and may negotiate profitable trade if opportunity arises banks are certain about targeted reserve balances and there is no risk of default intermediation emerges in the equilibrium Heider, Hoerova, Holthausen (WP, 2009) version of Diamond and Dybvig (1983) model competitive market in presence of a counter-party risk due to asymmetry in information market can break down with banks hoarding cash 6 / 57
A Model of Network Formation for the Overnight Interbank Market Introduction Interbank Market One day Lending/Borowing on eMID 7 / 57
A Model of Network Formation for the Overnight Interbank Market Introduction Interbank Market This Model: banks face uncertainty about their reserves and have an option to access the interbank market banks form bilateral agreements about loan size and interest rate there is a default risk concept of pairwise stable equilibrium network there will be no intermediation in the equilibrium and a possibility of market breakdown 8 / 57
A Model of Network Formation for the Overnight Interbank Market Model Plan Introduction 1 Interbank Market Model 2 Variables and payoffs Solution Equilibrium Network Configurations Interest Rate Discussion and Extensions 3 Empirics of Interbank Networks Core-Periphery Structure Policy Implications Systemic Risk and Network Approach Conclusion 4 9 / 57
A Model of Network Formation for the Overnight Interbank Market Model The model 10 / 57
A Model of Network Formation for the Overnight Interbank Market Model Intuition: a trading network Consider any connected network of trading opportunities over some goods. In equilibrium every node will have the same marginal rate of substitution between goods: sort of contagion? Even more so if the network is endogenous: and it will be generically connected 11 / 57
A Model of Network Formation for the Overnight Interbank Market Model Variables and payoffs Environment We model one day (night) Central Bank and N banks Central Bank maintains a Corridor System: T i reserve holdings on bank i r p penalty rate at which any bank can borrow from the Central Bank r d deposit rate of the Central Bank r p > r d Banks manage their reserves (“cash”) and use overnight market for lending and borrowing 12 / 57
A Model of Network Formation for the Overnight Interbank Market Model Variables and payoffs Variables Exogenous variables s i initially expected reserve holdings of bank i F i CDF of an error made in prediction of the reserves s i + ε i actual reserve holdings (net of interbank market) q i probability of default on interbank loan of bank i (known to all) Endogenous variables Banks lend money to each other to achieve C i expected reserve holdings of bank i afer interbank trade As a result banks create a directed network g = ( L , r ) with L lending matrix, ℓ ij ∈ R + is an amount lent by i to j for each ℓ ij > 0 we have an interest rate r ij ≥ 0 13 / 57
A Model of Network Formation for the Overnight Interbank Market Model Variables and payoffs Reserve Holdings With interbank lending: projected reserves of bank i are � � C i ( g ) ≡ s i − k ∈ N ℓ ik + m ∈ N ℓ mi . � �� � � �� � Lending Borrowing actual reserve holdings of bank i � � ( s i + ε i ) − k ∈ N ℓ ik + m ∈ N ℓ mi = C i ( g ) + ε i 14 / 57
A Model of Network Formation for the Overnight Interbank Market Model Variables and payoffs Expected Payoffs Expected payoff with the Central Bank: � T i − C i � ∞ � � � � π CB r p dF i ( ε i )+ r d dF i ( ε i ) = − T i − ( C i + ε i ) ( C i + ε i ) − T i i T i − C i −∞ Expected marginal rate of bank i from CB transactions is W i := r d + ( r p − r d ) F i ( T i − C i ) . 15 / 57
A Model of Network Formation for the Overnight Interbank Market Model Variables and payoffs Expected Payoffs: Interbank market Banks can enter the interbank market : borrowers can get lower interest rate lenders can get higher interest rate Assumption ( Exogenous Default ) Bank i has a probability of default on loan, q i ∈ [ 0 , 1 ] . It is independent of banks’ reserves and known to every bank. Defaults of different banks are independent events. Assumption ( Consequences of Default ) If a borrower defaults, then the lender will not receive its loan (neither principal nor interest) back. If a lender defaults, the borrower still has to pay the principal and loan. 16 / 57
A Model of Network Formation for the Overnight Interbank Market Model Variables and payoffs Expected Payoffs: Interbank market Assumption ( Consequences of Default ) If a borrower defaults, then the lender will not receive its loan (neither principal nor interest) back. If a lender defaults, the borrower still has to pay the principal and loan. � � � π IM r ik ℓ ik ( 1 − q k ) − − = ℓ ik q k ℓ mi r mi i k ∈ N k ∈ N m ∈ N � �� � � �� � � �� � interest due from losses because of interest due to repaying borrowers defaulted borrowers lenders 17 / 57
A Model of Network Formation for the Overnight Interbank Market Model Variables and payoffs Expected Payoffs: Summary Bank maximizes the total expected profit: q i B + ( 1 − q i ) π i , or, equivalently, π i = π CB + π IM = i i � T i − C i � ∞ � � � � r p dF i + r d dF i = − T i − ( C i + ε i ) ( C i + ε i ) − T i T i − C i −∞ � � � + r ik ℓ ik ( 1 − q k ) − ℓ ik q k − ℓ mi r mi k ∈ N k ∈ N m ∈ N Expected marginal rate of bank i from CB transactions is W i := r d +( r p − r d ) F i ( T i − C i ) = r p F i ( T i − C i )+ r d � � 1 − F i ( T i − C i ) , from borrowing − r mi from lending r ik ( 1 − q k ) − q k 18 / 57
A Model of Network Formation for the Overnight Interbank Market Model Variables and payoffs Pairwise Stable Networks For every possible network g , banks can compute their total expected profits, π i . Which network do we expect to see? 19 / 57
A Model of Network Formation for the Overnight Interbank Market Model Variables and payoffs Pairwise Stable Networks For every possible network g , banks can compute their total expected profits, π i . Which network do we expect to see? Definition Network g = ( L , r ) is a pairwise stable equilibrium if: a pair of banks (a borrower and a lender) set the quantity/rate ( L , r ) of their loan such that it is Pareto optimal for them given the rest of the network if L = 0 , there no link and r is not defined 19 / 57
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