OFFICE OF FINANCIAL RESEARCH How Lkely Is Contagon n Fnancal Networks? Paul Glasserman & Peyton Young Systemc Rsk: Models and Mechansms Isaac Newton Insttute, Unversty of Cambrdge August 26-29, 2014 Ths presentaton represents the vews of the authors and not the offcal vews of the
Overvew We show how to estmate the probablty of contagon and the ncrease n expected losses due to contagon wth vrtually no knowledge of the network topology. Ths s mportant because n practce detals of nterbank network exposures are not known wth much precson and they are constantly n flux. Key parameters needed for the analyss bank sze (assets) bank leverage proporton of labltes to the nonfnancal sector proporton of assets from the nonfnancal sector 1 Ths presentaton represents the vews of the authors and not the offcal vews of the
Prevew of results If all banks have the same sze, the probablty of contagon s less than the probablty of drect default for a wde class of shock dstrbutons regardless of the network topology. Expected losses due to ndrect (domno) effects are typcally small compared to the expected losses from shocks to the frm s own assets. The rato of the two effects can be bounded wthout knowng the detals of the network. Bankruptcy costs and mark-to-market wrte-downs n advance of default ncrease the probablty of contagon and the expected sze of the losses. These can be estmated usng smple formulas that do not depend on the network topology. 2 Draft / Senstve / Pre-Decsonal For Dscusson Purposes Only
The Fnancal Network and the Outsde World Outsde ( real ) world Outsde assets c (e.g, mortgages, commercal loans) Outsde labltes b (e.g, deposts) 3 Ths presentaton represents the vews of the authors and not the offcal vews of the
Insde the Network Payments due from node k j k pa k k pa j Payments due to node j Outsde assets c Outsde labltes b 4 Ths presentaton represents the vews of the authors and not the offcal vews of the
What We See pa k k k pa j j Outsde assets c Outsde labltes b assumed > 0 5 Ths presentaton represents the vews of the authors and not the offcal vews of the
Key parameters Net worth Leverage of outsde assets : outsde assets/net worth λ = c / w Fnancal connectvty : n-network labltes/total labltes β = ( p - b)/ p Contagon ndex : βw ( λ 1) 6 Ths presentaton represents the vews of the authors and not the offcal vews of the
Weak contagon We compare the probablty of ndrect falure due to contagon wth the probablty of drect falure due to wrte-downs n a bank s outsde assets. Contagon from bank to a set of banks D s weak f the nodes n D are more lkely to default through ndependent drect shocks to ther outsde assets than through an ndrect shock from. 7 Ths presentaton represents the vews of the authors and not the offcal vews of the
Theorem on weak contagon Let d = D λ = λ d = λ 1 1 D [( j ) / )] harmonc mean of the j' j D w = ( w ) / d = arthmetc mean of w ' s D j j j D s Theorem: Suppose the shocks are..d. beta dstrbuted. Contagon from to D s weak f λ w β w( λ 1). (1) D D Contagon from to D s mpossble f j D w β w( λ 1). (2) j Note that the rght-hand sde s the contagon ndex, whch measures the mpact of shocks to on the rest of the fnancal system. 8 Ths presentaton represents the vews of the authors and not the offcal vews of the
Corollary If all banks have the same amount of outsde assets, contagon from any node to any set of nodes s weak. Hence wthout some degree of heterogenety contagon s weak rrespectve of the topologcal structure of the nterbank network. 9 Ths presentaton represents the vews of the authors and not the offcal vews of the
How much do nterbank connectons amplfy losses? At each node, replace the n-network assets and labltes wth fcttous out-of-network assets and labltes, thus preservng the net worth of each node whle amputatng all nterbank connectons. Assume (conservatvely) that the fcttous out-of-network assets are not vulnerable to shocks. Usng the same shock dstrbuton compare expected losses n the orgnal network wth expected losses n the amputated network. pa k k k pa j j Outsde assets c Outsde labltes b 10 Ths presentaton represents the vews of the authors and not the offcal vews of the
Loss amplfcaton due to network X = shock to 's outsde assets o L = X = losses wthout network effects L = losses wth network effects δ = P( X > w ) = probablty that defaults drectly + β = max β = maxmum fnancal connectvty Theorem. Suppose the relatve shocks X / c have a common log - concave dstrbuton. Then δc EL [ ] 1+ o EL [ ] (1 β + ) 1/(1 - ) I ) s the amplfcaton factor due to fnancal connectvty 11 Ths presentaton represents the vews of the authors and not the offcal vews of the c
Other Factors Leadng to Contagon Mark-to-market losses from credt deteroraton: a loss of confdence n one bank s ablty to meet ts oblgatons cascades through the network Bankruptcy costs: Falure produces losses above and beyond payment shortfall (delays, ltgaton, etc.) Fre sales 12 Ths presentaton represents the vews of the authors and not the offcal vews of the
Bankruptcy costs Every $1 of default n payments causes an addtonal $γ n bankruptcy costs Slope 1+γ 13
Credt qualty deteroraton Orgnal model Modfed 14 Draft / Senstve / Pre-Decsonal For Dscusson Purposes Only
Network effects wth bankruptcy costs European Bankng Authorty stress test data (2010). = 0.43, γ = 0.50 If δ = 1%, the network adds 4.2% to expected losses 15 Ths presentaton represents the vews of the authors and not the offcal vews of the
Summary The contagon ndex measures the mpact that the falure of a gven bank has on the fnancal system. The probablty that a gven bank causes a group of szable banks to fal due to contagon s less than the probablty that the group defaults drectly unless has a suffcently hgh contagon ndex. If all banks are the same sze as measured by outsde assets, the probablty of contagon s less than the probablty of drect default for a wde class of shock dstrbutons regardless of the network topology. 16 Ths presentaton represents the vews of the authors and not the offcal vews of the
Summary (contnued) Losses due to pure spllover effects n the network are typcally small compared to the losses from drect default. Bankruptcy costs and mark-to-market wrte-downs n advance of default ncrease the probablty of contagon and the expected sze of the losses. Losses attrbutable to network effects can be bounded wthout knowng the detals of the network. These losses are amplfed by the degree of fnancal connectvty, whch s a key ndcator of systemc stablty. 17 Ths presentaton represents the vews of the authors and not the offcal vews of the
Selected references Ths paper: Paul Glasserman and H. Peyton Young, Journal of Bankng and Fnance http://www.scencedrect.com/scence/artcle/p/s0378426614000600 Earler verson: Workng Paper 9, Offce of Fnancal Research, U.S. Treasury Department. Other network contagon models: Esenberg and Noe 2001; Ga and Kapada 2010, 2011; Amn, Cont and Mnca 2010; Acemoglu, Ozdaglar, and Tahbaz-Saleh 2013; Ellott, Golub, and Jackson 2013; Cabrales, Gottard, and Vega-Redondo 2013. 18 Ths presentaton represents the vews of the authors and not the offcal vews of the
Thank You! 19 Draft / Senstve / Pre-Decsonal For Dscusson Purposes Only