Youth Employment, Camps and Activities Guide - NUPACE
Transcript of Youth Employment, Camps and Activities Guide - NUPACE
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Illiquidity in Financial Networks
Maryam Farboodi
May 17, 2013
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Outline
Introduction
Model
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Motivation
I Contagion and systemic risk
I A lot of focus on bank inter-connections after the crisis
I Too-interconnected-to-failI Interconnections:
I Propagate a shock from a bank to many banksI Exposes banks to counterparty risk
I Reasonable to study bank inter-connections in a netorksetting
I Focus on Counterparty risk: negative spillover betweenbanks
I Can induce run on banks in certain states
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
This Paper!
I Focuses on network formation among banks
I Externalities that banks form the ”wrong” networkI Classic externality: Each bank does not fully internalize
the failure of others due to his failureI Equilibrium social surplus and on profit hurt
I What I want to address: Change in division of surplusI Each bank does not care to hit the social surplus as
long as his own share increases
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Network Literature
I How does a negative shock propagate through thenetwork?
I Can the network structure amplify a shock?
I A lot of work on random networks
I Some recent work focusing on contagion given thenetwork structure
I Very little done on strategic network formation amongbanks
I Network on a ringI Even less when counter party risk is involved
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
What is Difficult? :D
I What is a link between two banks (financialinstitutions)?
I Superposition of at least three networks:I OTC derivativesI Bilateral lendingI Common asset holding
I Complex interaction between the three, banks adjust ondifferent margins
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Evidence
I Data: bilateral exposures not really knownI OTC network: approximately a core-periphery networkI Interconnected coreI Core banks (”dealers”) low net exposure, high grossI peripheries net lenders
Figure : OTC bank exposures as a Core-Periphery model
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Financial Network
I Directed Graph G (N,E )I Nodes are banks {i , j}I Edges are lending eij : i has lent to j
Figure : Simple interbank lending network with 5 banks
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Basic Idea
I i and j choose to enter a lending relationship (edge eijadded to the network) if
Φi (G + ij) > Φi (G )
Φj(G + ij) > Φj(G )
I Has nothing to do with∑k
Φk(G + ij) >∑k
Φk(G )
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Equilibrium Concept: Stability
I Pairwise StabilityI No node prefer to unilaterally break a connectionI No pair of nodes prefer to add a connection
I Coalitional StabilityI No coalition of nodes want to deviate
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Outline
Introduction
Model
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Environment
I 4 dates t = 0, 1, 2, 3I 4 banks
I 2 with risky investment opportunity (R1,R2)I 2 without (S1,S2)
I No discounting
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Bank Choice Set
I Bank with investment opportunityI From/to which banks borrow/lend (size fix)I How much liquidity to holdI Invest in long term h(.)
I Bank without investment opportunityI To which banks lendI Invest in h(.)
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Timeline
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Banks
I Each bank has charter value V i , i ∈ {R, S}I Each bank has raised one unit from uninformed passive
outside investors
I Banks can lend to each other
I All borrowing of the form of 1-period debt
I Universal risk neutrality
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Technology
I Risky AssetI Investment I at date 0I Can be of three types U,M,BI Liquidity shock ρ ∈ {+αI , 0,−αI} at date 2
I iid across the two investments
I Can be liquidated at date 1 for LI Return realized at date 3 if not liquidated and potential
liquidity need metI Gk(R) ∼ [0, R̄], k ∈ {U,M,B}
I If debt not met: bankruptcy and return is destroyed
I Safe long term asset: h(.) concaveI Safe final returnI No intermediate liquidity need
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Asset Random Type
Type Probability Liquidity Shock (ρ) Return Dist.B p −αI GB(.)/0M p1 0 GM(.)U 1− p − p1 αI GU(.)
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Information
I Each bank knows own and counterparty liquidity needat date 1
I Can withdraw short term debt
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Assumptions
I Each bank can borrow from at most two banks
I Each bank can not allocate more than half of it’sresources to any use (lend/risky investment/safe longterm investment/etc)
I Each bank can lend 0.5 to any other bank
I If invest I , can choose to hold θ ∈ {αI , 0} liquidity
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Risky Bank R1 Balance Sheet
Liabilities Assets (= A)
1 IbS1R1 ∈ {0, 1
2} θ ∈ {αI , 0}bS2R1 ∈ {0, 1
2} h(A− I − θ)bR2R1 ∈ {0, 1
2} bR1R2 ∈ {0, 12}
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Link Formation Process
I Each bank chooses a set of links to form(lend andborrow):
{{ei .}, {e.i}
}I Connection formed
I Borrower chooses the amount of liquidity to holdI Lender chooses the face value of debt
I The face value would be such that if accepted, in theinduced equilibrium it maximizes the surplus which goesto lender
I Can not offer to borrow from more than two banks
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Possible Outcomes
Figure : Possible Outcome Networks
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Equilibrium Concept: Stability
I Pairwise StabilityI No node prefer to unilaterally break a connectionI No pair of nodes prefer to add a connection
I Coalitional StabilityI No coalition of nodes want to deviate
I I will only consider symmetric equilibria for now
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Intuition
I Risky bank can affect the realized distribution of returnthrough inducing a run in certain states
I Run can be induced through
I Run erodes some surplus, but also change thedistribution of surpus
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Asset Random Type
Type Probability Liquidity Shock (ρ) Return Dist.B p −αI GB(.)/0M p1 0 GM(.)U 1− p − p1 αI GU(.)
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Division of Surplus
I Resources in short supply
I lender must be payed maximum amount
D∗ = arg maxD
D(1− G (D))
S =
∫ R̄
D∗Rg(R)dR
L = D∗(1− G (D∗))
B =
∫ R̄
D∗(R − D∗)g(R)dR
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Example. Division of Surplus
Figure : Division of Surplus among lender and borrower at theface value which maximizes lender share. Plot is made for returndistribution family is G n(R) = Rn
R̄n ∼ [0, R̄].
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Excessive Exposure to Counterparty Risk
I Risky bank dislikes the eventual division of surplus in Mbut likes it in U
I Connect to the other risky and not holding any liquidity
I Chance of failure in M due to counterparty failure
I Preventive run by safe lender at date 1
I Some surplus destructed, but the division of the resttilted towards risky banks
Illiquidity inFinancial Networks
Maryam Farboodi
Introduction
Model
Results
I I show that under some parameter values, risky banksover connect
I Equilibrium network is such thatI Connections between risky banks create counterparty
riskI Counterparty risk destroys social value (too much run)I Risky banks get a bigger share of the realized social
value at the expense of othersI So they have an incentive to form those connections in
the first place
I Adding even less informed outsiders amplifies the losses