Financial networks and default-driven shocks:

an application to banking systems

Francisco Hawas (*)Research Assistant

Mathematical Modeling CenterUniversidad de Chile

(*) Joint project with Arturo Cifuentes and Alejandro Jofré

Motivation

• Financial crisis (2007-2008)– Size of banks?– Number of banks?– Degree of Interconnections?• Direct• Indirect

• Regulatory and academic interest on the topic of financial networks

Overview

• Problems from the financial regulator viewpoint:– Liquidity risk

• Inability to pay, not necessary a balance sheet problem

– Solvency risk• Balance sheet problem

• This project will focus, initially, on the solvency aspects – Liquidity will be left for a second stage

Bank’s Balance sheet

Assets Liabilities

Cash, Ck

Loans to third parties, Lk

Loans to other banks, Bk

Deposits at CB, θ Dk

Investments, Ik

Deposits, Dk

Equity, Ek

Debt to CB, Фk

Debts to other banks, Hk

Model Overview

• Define balance sheet parameters:– , L, D, I, Ф, H, E, Θ

• Define interconnection parameters– β, ρ– Direct connections between banks• : percentage of bank’s debt that bank owns• ; : number of banks

– Indirect connections• : correlation through loans (L)

Bank 1

Bank N

Gaussian Copula [ε, ρ]

Loans to third parties

𝐿𝑡1=𝐿𝑡 −11 (1−𝜀𝑡1 )

Indirect connection

𝐿𝑡𝑁=𝐿𝑡− 1𝑁 (1−𝜀𝑡𝑁 )

Model Overview

• At time :– Simulate

• : default loss• Gaussian Copula• Uniform marginals

– Update

•

– If bank has , then defaults• goes out of the simulation• Update • Loop until

– Next period

Model Overview

𝜀1

𝐸1≤0?

𝜀2

Bank k such that will continue in the simulation

End point:1) All Banks have

defaulted2) End of simulation

time

𝐿1=𝐿0 (1−𝜀1 ) 𝐿2=𝐿1 (1−𝜀2 )

Example

• Parameters:– : 5%– : 30%– Θ: 0– Equity ratio: 10%– All balance sheets are the same

Number of Banks 20 40 60

Number of connections 2 10 16 4 20 32 6 30 48

Time to first default (Mean)

14 14 14 12 12 12 13 13 13

Example

• Parameters:– : 5%– : 30%– Θ: 0– Equity ratio: 8%-12%– All balance sheets are similar (Just Equity ratio differs)

Number of Banks 20 40 60

Number of connections 2 10 16 4 20 32 6 30 48

Time to first default (Mean)

14 12 14 10 12 10 12 13 12

Topics to investigate

• Influence of balance sheet structure– Leverage ratio

• Central Bank policy– Effect of Θ– Rescue loan policy

• Effects of number of banks– No diversification effects?

• Effects of number of connections– Selection of counterparty is random

Important questions to be answered

• Does diversification improve system resilience?• Is interconnection (degree of) harmful for the

financial system? • Importance of correlation at a fundamental level…

important?• Is the dynamics of correlation important? – Steady, peak, steady, relevant?

• What would be the effect of a run on a bank? Or the system? At which speed the system turn into unstable mode?