Youth Employment, Camps and Activities Guide - NUPACE

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Illiquidity in Financial Networks Maryam Farboodi Introduction Model Illiquidity in Financial Networks Maryam Farboodi May 17, 2013

Transcript of Youth Employment, Camps and Activities Guide - NUPACE

Page 1: Youth Employment, Camps and Activities Guide - NUPACE

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Illiquidity in Financial Networks

Maryam Farboodi

May 17, 2013

Page 2: Youth Employment, Camps and Activities Guide - NUPACE

Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Outline

Introduction

Model

Page 3: Youth Employment, Camps and Activities Guide - NUPACE

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

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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

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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

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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

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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

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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

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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 )

Page 10: Youth Employment, Camps and Activities Guide - NUPACE

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

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Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Outline

Introduction

Model

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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

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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(.)

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Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Timeline

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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

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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

Page 17: Youth Employment, Camps and Activities Guide - NUPACE

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(.)

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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

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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

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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}

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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

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Illiquidity inFinancial Networks

Maryam Farboodi

Introduction

Model

Possible Outcomes

Figure : Possible Outcome Networks

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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

Page 24: Youth Employment, Camps and Activities Guide - NUPACE

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

Page 25: Youth Employment, Camps and Activities Guide - NUPACE

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(.)

Page 26: Youth Employment, Camps and Activities Guide - NUPACE

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

Page 27: Youth Employment, Camps and Activities Guide - NUPACE

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].

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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

Page 29: Youth Employment, Camps and Activities Guide - NUPACE

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