Download Monetary Policy Model

Macrofinancial Risk Analysis Using
Contingent Claims Analysis (CCA) for
Financial Stability, Linking Financial
Sector to Monetary Policy Models
Dale Gray
Monetary and Capital Markets Department
International Monetary Fund
[email protected]
The views expressed in this presentation are those of the author and should
not be attributed to the International Monetary Fund, its Executive
Board, or its management.
Outline

Contingent Claims Analysis (CCA)
– CCA Framework and Models
– Application to Financial Institutions
• Recent Sub-prime Crisis
• CCA for Icelandic Banks


CCA Models Linked to Factor Models and
Monetary Policy Models (application to Chile)
Sovereign Economy-wide CCA Models
Presentation based on ongoing research Dale Gray; and papers by
Dale Gray, Robert C. Merton and
Zvi Bodie in: (i) JOIM
2007, (ii) NBER 2007; and (iii) new book on Macrofinancial
Risk Analysis (2008).
2
Macrofinancial Risk Analysis


Framework integrates riskadjusted balance sheets
using Contingent Claims
Analysis (CCA) with
macroeconomic and
monetary policy models
CCA models of financial
institutions, corporates,
and sovereigns are
integrated together and
with macroeconomic
models
3
Linking CCA Balance Sheet Models to
Macroeconomic Flows and Models




Macroeconomic models geared to try to forecast
the mean of macro variables (i.e. first moment)
Finance measures risk from stochastic assets
relative to threshold (second and third moments
critical to risk indicators).
CCA is an excellent tool for analyzing financial
stability
Time pattern of CCA risk indicators can be linked
to macroeconomic variables and to monetary
policy models
4
Core Concept: Merton Model/CCA for Firms and Banks
Assets
Equity
or Jr
Claims
Risky
Debt
Assets =
Equity
=
Equity
+
+
• Value of liabilities
derived from value of
assets.
• Liabilities have
different seniority.
• Randomness in
asset value.
Risky Debt
Default-Free Debt – Expected Loss
= Implicit Call Option + Default-Free Debt – Implicit Put Option
5
CCA Credit Risk Measures
Asset
Value
Exp. asset
value path
Distribution of Asset Value
Distance to
Distress:
standard
deviations asset
value is from
debt distress
barrier
V0
Distress Barrier
or promised payments
Probability of Default
T
Time
6
CCA models of the Financial Sector and links to Macro
Models

Decomposing factors driving bank CDS spreads
– Leverage, asset volatility, Global market risk
appetite, loss given default
– Implicit put options as a measure of risk



Linking credit risk indicators to macro models. Factor
models of CCA asset and risk indicators for systemic
stress testing and link to GDP growth
Integrating financial sector with monetary policy
models
Analysis of non-linear risk transmission between key
sectors in an economy-wide CCA balance sheet model
7
Calibrating Implied Assets and Asset Volatility
Implied asset value and implied asset volatility
calibrated from contingent claims analysis.
Merton
Model
Moody’s-KMV
for firms and financial institutions
Merton-type
CCA or hybrid models have been applied to corporates
and financial institutions. Moody’sKMV, Kamakura and others have
applied these models for credit risk analysis to tens of thousands of
firms and banks in over 50 countries around the world.
MKMV
provides daily output for 37 financial institutions in Sweden
Calibration
using equity options
Another
way to implement the Merton model is to use information
from equity options (implied volatility and “skew”) to calculate credit
risk and spreads in banks in US, Sweden and other countries.
8
Calibrate (Unobservable) Market Value of Asset and
Implied Asset Volatility
USING TWO EQUATIONS
WITH TWO UNKNOWNS
INPUTS
Value and
Volatility of Market
Capitalization, E

Debt Distress
Barrier B (from
Book Value)


Time Horizon
E  A N (d1 )  Be rt N (d 2 )
E E  A A N (d1 )
Gives:
Implied Asset
Value
A
and
Asset Volatility A
Default Probabilities
Spreads, Risk Indicators
KMV maps risk indicators to actual default
probabilities (EDFs) using historical default data
9
MKMV Key Drivers of Expected Default Frequency
(EDF) and EDF Implied CDS spreads (EICDS)
EDF Key Drivers are Market Leverage (default point
divided by assets) and asset volatility
EDF  f ( LMkt Leverage ,  Asset , other )
Key Drivers of EICDS are Risk-Neutral EDF (from EDF,
Market Sharpe Ratio (SR), correlation ρ)
and Loss Given Default
EDFRisk  Neutral  f  EDF ,  A, Mkt , SR 
1
EICDS   ln 1  LGDRisk  Neutral * EDFRisk  Neutral 
T
10
What does CCA/MKMV Have to Say About Subprime
Crisis? –First, See evolution of market CDS Spreads over the
2007-2008 Crisis for Major US banks and Primary Dealers
400
350
Goldman Sachs
300
Bear Stearns
Merrill Lynch
250
Lehman Brothers
Citigroup
200
JP Morgan
Bank of America
150
Morgan Stanley
Deutsche Bank
100
Credit Suisse
UBS
Barclays
50
7/11/2008
5/12/2008
3/13/2008
1/13/2008
11/14/2007
9/15/2007
7/17/2007
5/18/2007
3/19/2007
1/18/2007
0
11
Market
Leverage Has
Increased
135
130
125
120
Bear Stearns
Lehman
Merrill
Citi
JPM
UBS
115
110
105
100
140
135
130
125
7/31/2008
6/11/2008
4/22/2008
3/3/2008
1/13/2008
11/24/2007
10/5/2007
8/16/2007
6/27/2007
95
Implied Asset
Volatility Has
Increased
Bear Stearns
Lehman
120
Merrill
115
Citi
JPM
110
UBS
105
7/31/2008
6/11/2008
4/22/2008
3/3/2008
1/13/2008
11/24/2007
10/5/2007
8/16/2007
95
6/27/2007
100
6/30/2007=100
12
Banks in Subprime Crisis – CCA/MKMV Implied Market
Value of Assets, June 30, 2007=100
130
120
Bear Stearns
110
Lehman
100
Merrill
Citi
90
JPM
80
UBS
70
7/31/2008
6/11/2008
4/22/2008
3/3/2008
1/13/2008
11/24/2007
10/5/2007
8/16/2007
6/27/2007
60
Assets increase Aug 2007 to early 2008 because of
SIV etc. assets brought back on to balance sheets ?
13
7/31/2008
6/11/2008
4/22/2008
3/3/2008
7/31/2008
6/11/2008
EDF Has
Increased
1/13/2008
700
11/24/2007
800
10/5/2007
900
8/16/2007
3/3/2008
4/22/2008
1000
6/27/2007
EICDS (Baisis points)
1/13/2008
11/24/2007
10/5/2007
8/16/2007
6/27/2007
EDF, one-year (in percent)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Bear Stearns
Lehman
Merrill
Citi
JPM
UBS
EDF Implied
CDS
Bear Stearns
Lehman
600
Merrill
500
Citi
400
JPM
UBS
300
Freddie
Fannie
200
100
0
14
Significantly Higher Market Sharpe Ratio since July
2007, with peaks on 3/27/08 and 8/6/08
1
0.9
0.8
0.7
0.6
0.5
8/10/2008
5/2/2008
1/23/2008
10/15/2007
7/7/2007
3/29/2007
12/19/2006
9/10/2006
6/2/2006
2/22/2006
11/14/2005
8/6/2005
4/28/2005
1/18/2005
10/10/2004
7/2/2004
3/24/2004
0.4
Market Sharpe Ratio and other indicators show
decreased risk appetite
15
Changes in Bank CDS due to Leverage, Volatility and Impact of
Increase in Market Price of Risk as of March 20, 2008
(Lower Risk Appetite, Higher Correlation)
With Subprime
Exposure/Loss
CDS January
2007
Without
Subprime Loss
18
20
Increased
Market
Leverage
+52
+45
Change in
Volatility
+41
+10
Market Price of
Risk Increase
(SR*ρ)
+75
+70
190 bps
145 bps
CDS March
2008
16
Icelandic banks and government– Questions and
issues that CCA can help with
What does the equity market vs the CDS market say
about credit risk in Icelandic banks?
What are implied asset and asset volatility and EDFs?
How has the change in global market risk appetite
affected CDS spreads in Iceland?
What are the differences in credit risk from the equtiy
market vs the CDS market? illiquidity of CDS?,
What does this mean for the contingent liabilities of the
Central Bank (liquidity support) and what does it
mean for government?
17
Icelandic Banks CCA Using MKMV
Implied Assets and Defaut Point
6000000
5000000
4000000
3000000
2000000
1000000
0
Implied Asset
LANDSBANKI
ISLANDS HF
GLITNIR
BANKI HF
KAUPTHING
BANK HF
Default Point
18
Icelandic Banks CCA Using MKMV
Implied Asset
Default Point
Leverage Ratio (%)
Implied Asset Volatility
EDF
EICDS
KAUPTHING BANK HF GLITNIR BANKI HF LANDSBANKI ISLANDS HF
5567530
2910099
3142737
3887411
1870303
2460756
70
64
78
3.4
4.2
3.4
0.03
0.04
0.1
1131
1016
553
19
8/22/2008
8/8/2008
7/25/2008
7/11/2008
6/27/2008
6/13/2008
5/30/2008
5/16/2008
5/2/2008
Landsbankinn
4/18/2008
4/4/2008
3/21/2008
3/7/2008
2/22/2008
2/8/2008
1/25/2008
Kaupþing
1/11/2008
12/28/2007
12/14/2007
11/30/2007
11/16/2007
Glitnir
11/2/2007
10/19/2007
10/5/2007
9/21/2007
9/7/2007
8/24/2007
8/10/2007
7/27/2007
7/13/2007
6/29/2007
6/15/2007
6/1/2007
Basis points
5 year senior CDS spreads - Icelandic banks and sovereign
01. June 2007 to 20. August 2008
-Source: Bloomberg-
1,200
Iceland government
1,000
800
600
400
200
0
20
12/18/2008
6/1/2008
11/14/2007
4/28/2007
10/10/2006
3/24/2006
9/5/2005
2/17/2005
Percent (Default Barrier divided by
Market Value of Assets)
Iceland Banks CCA
Market Leverage
85
80
75
KAUPTHING BANK
HF
70
65
GLITNIR BANKI
HF
60
55
LANDSBANKI
ISLANDS HF
50
21
Iceland Banks CCA
10
9
8
7
6
5
4
3
2
1
0
KAUPTHING BANK
HF
GLITNIR BANKI
HF
12/18/2008
6/1/2008
11/14/2007
4/28/2007
10/10/2006
3/24/2006
9/5/2005
LANDSBANKI
ISLANDS HF
2/17/2005
MKMV Asset Volatility
MKMV Asset Volatility
22
Issues regarding differences in information from CDS
and Equity markets for Icelandic banks
What does the equity market vs the CDS market
say about credit risk in Icelandic banks?


Take observed market CDS an get implicit Put
option (PCDS)
Then take equity information and get implicit Put
Option (PEQ)
What are the explanations for the differences?
illiquidity of CDS?, illiquidity of equity?, other?
What does this mean for the contingent liabilities
of the Central Bank (liquidity support) and what
does it mean for government?
23
CCA models of the Financial Sector and links to Macro
Models

Decomposing factors driving bank CDS spreads
– Leverage, asset volatility, Global market risk
appetite, loss given default
– Implicit put options



Linking credit risk indicators to macro models. Factor
models of CCA asset and risk indicators for systemic
stress testing and link to GDP growth
Integrating financial sector with monetary policy
models
Analysis of non-linear risk transmission between key
sectors in an economy-wide CCA balance sheet model
24
Bank-by-Bank CCA and Factor Models for Stress-Testing
Proceedure:

Calibrate CCA model for each bank

Estimate factor model for bank return

Generate scenarios and carry out stress test to see
impact on bank credit risk and on equity capital
Step 1
Scenario
generation
(global and
domestic
factors)
Step 2
Factor
Model for
bank asset
return
(or bank risk
indicators)
Step 3
CCA model
for each
bank
(or bank
group)
Step 4
Impact on
bank credit
risk, (POD,
implicit put,
spread) and on
equity capital
25
EXAMPLE OF CHILE BANK FACTOR MODEL - Banks have
Heterogeneous Response to Individual Factors; Stress testing can
be with individual factors or with Four Principal Components
Factors associated with different components of asset returns
Factor 1 1
Factor
Factor
2
Factor
3
Factor
2
Factor 43
Factor
VIX
S&P
IPSA
CLP / USD
U.S. Rates
Yld Curve 10-Yr (Chg)
1-Yr (Lvl)
1-Yr (Chg)
Chile CPI
Oil
Copper
US CPI
Factor
5
Factor
4Factor 6
IMACEC Chile Unemp.
Chile CPI CLP / BRL
Copper
Scenario 1: Shock to Financials Variable Comparable to 2003
7%
6%
Default Probability
Financials
5%
U.S. Rates
(Levels)
Change
Cyclicals
Domestic
Domestic/
Regional
4%
3%
2%
1%
26
0%
1
4
7
10
13
16
CCA models of the Financial Sector and links to Macro
Models

Decomposing factors driving bank CDS spreads
– Leverage, asset volatility, Global market risk
appetite, loss given default
– Implicit put options



Linking credit risk indicators to macro models. Factor
models of CCA asset and risk indicators for systemic
stress testing and link to GDP growth
Integrating financial sector with monetary policy
models
Analysis of non-linear risk transmission between key
sectors in an economy-wide CCA balance sheet model
27
CCA Risk Indicators in Monetary Policy Models
The integration of the financial sector vulnerability into
macroeconomic models is of keen interest for
policymakers.
Explicit inclusion of CCA sytemic credit risk/financial
fragility indicator

Should a financial fragility indicator be included in
monetary policy models?
– Yes, at least in the GDP Output Gap equation

Should it be explicitly included in the reaction
function? Or, should the central bank react only
indirectly through reacting to its effects on output
gap and inflation?
– Depends
28
CCA Chilean Banking System Risk and Macro
Effects
GDP is affected by financial stability in the
banking system via


Financial accelerator links;
Financial distress in banks and bank’s
borrowers reduces lending as borrower’s
credit risk increases, which reduces
investment and consumption affecting GDP.
29
Chilean Banking System – CCA Distance-toDistress (DTD) is Estimated for Banking System
12
DTD of Banking System
Output Gap
10
8
6
4
2
1997M01
0
1999M01
-2
2001M01
2003M01
2005M01
2007M01
-4
-6
DTD has significant impact on
Output Gap
30
DTD related to GDP Growth for Chile
yt  c  1rt 1   2 dtdt 1   3et 1   4 yt 1   t
Sample: 1998 2007 (monthly)
Included observations: 106 after adjustments
Variable
C
R(-1)
DLOG(E(-1))
DLOG(DTD(-1))
DLOG(Y(-1))
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
Coefficient
0.011
-0.001
0.046
0.012
0.463
0.574
0.557
0.008
0.007
358.890
1.912
Std. Error
t-Statistic
0.002
0.000
0.019
0.003
0.074
4.830
-3.723
2.438
3.551
6.283
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
Prob.
0.000
0.000
0.017
0.001
0.000
0.009
0.013
-6.677
-6.552
34.036
0.000
31
DTD related to Output Gap for Chile
gapt  c  1dtdt 1   2 et 1   4 gapt 1   t
Sample (adjusted): 1998M02 2007M02
Included observations: 109 after adjustments
Variable
C
DLOG(TCR(-3),0,3)
LOG(DTDS(-1))
YGAP(-1)
YGAP(-3)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
Coefficient
-1.736
4.134
0.934
0.513
0.225
0.661
0.648
0.712
52.766
-115.126
1.842
Std. Error
0.470
1.639
0.256
0.082
0.072
t-Statistic
-3.691
2.522
3.653
6.275
3.113
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
Prob.
0.000
0.013
0.000
0.000
0.002
-0.035
1.201
2.204
2.328
50.695
0.000
32
Simple Five Equation Monetary Policy Model
GDP Gap with Financial Sector DTD:
yt  1 yt 1   2 (rsd ,t  L   t  L )  3 X S ,t  L   4 dtdt  1,t
or
yt  yt *   4 dtdt  1,t
Traditional Taylor Rule:
rsd ,t  rd ,t 1  (1   ) ( (
e
t ,t T
  )  (1   ) yt )   4,t
T
Taylor Rule with Financial Stability Indicator:
rsd ,t  rd ,t 1  (1   ) ( ( te,t T   T )  (1   ) yt *)
 10 dtdt   4,t
33
Monetary Policy Model (cont.)
Inflation:
 t  5 t 1  6 yt  7 te,t T  8X S ,t  9 sLCD   2,t
Exchange Rate:
X S ,t  11 X S ,t 1  12rsd ,t  13rsf ,t  14 st ,t T  15dtd   5,t
Yield Curve:
Rt  16 Rt  17 ( Rt 1  Rt )
 18 ( Rt 1  Rt ) t 1  19 (rt 1  rt )t   2,t
34
Impulse Response Functions (IRF) with
DTD in Monetary Policy Model
IRF is the standard tool to analyze the behavior
of a monetary model of this type (we are not
presenting standard deviations).
– For each period of time, the model solves a
system of equations for the current and
expected value of the main variables;
– The model works as expected: signs and
magnitudes seem reasonable;
– Financial Sector Distance-to-Distress (DTD)
has a significant impact on short and long
term interest rates, ER, and Output-Gap.
35
Impulse Response: Shock to banking sector distance to
default (DTD)
2.0%
dp
y
e
r
rl
ldtd
1.5%
1.0%
0.5%
0.0%
200004
200204
200404
200604
200804
201004
-0.5%
-1.0%
-1.5%
36
Efficiency Frontiers for the steady state
volatility of GDP and inflation
A base scenario is set where there is no
reaction of the monetary policy to DTD, but
GDP and exchange rate still react to it.
Shocks to DTD could be understood as shocks
to risk appetite.
Starting from a Base Model a higher reaction
to DTD and lower endogeneity are tested.
37
Efficiency Frontiers: Base Model if Monetary
Policy Rate reacts to Financial Sector DTD
3.5%
Output volatility
3.0%
2.5%
2.0%
1.5%
No Policy
MPR to DTD
1.0%
1.0%
1.5%
2.0%
2.5%
3.0%
Inflation volatility
38
Results and Conclusions of Chile CCA-Monetary Policy
Model Analysis
A simple, but powerful model for monetary policy
including financial sector risk indicator (DTD)
Empirical evidence supports the model. DTD affects
GDP growth and Output Gap
Impulse Responses in accordance with theory.
Robust efficient frontier, but there is a trade off in the
results:
A stronger reaction of policy interest rates to DTD
reduces inflation volatility, but increases output
volatility.
More analysis is being carried out.
39
Unified Macrofinance Framework
(Targets: GDP, Inflation, Financial System Credit Risk,
Sovereign Credit Risk)
Policies:
Domestic and
International
Factors
Sovereign
CCA Model
• Fiscal Policy
• Debt Management
• Reserves / SWF
Interest Rate
Term Structure
Model
Monetary
Policy Model
Financial CCA
(Merton-STV)
Model (s)
Economic Capital
Adequacy
• Policy Rate
CRI
• Economic Capital
Adequacy
• Bank and Financial
Sector Regulations
40
CCA Model of the Sovereign – Very Useful for Iceland

Sovereign Assets
– Present value of primary fiscal surplus
– Reserves
– Minus contingent liabilities to banks and others

Sovereign Liabilities
– Base money, foreign and local-currency debt
– Model measures sovereign spreads Note
exchange rate volatility and skew affects
sovereign spreads
41
Sovereign, Bank, and Corporate Economy-wide CCA
Sector Interlinked Balance Sheets
Risky Debt = Default-free Value of
Debt minus Expected Losses
Equity
Corporate
Sector
Assets
Default-free
Debt Value
– Put
Option
Money &
Sovereign
Assets
Local
Currency Debt
Expected losses in risky debt are
implicit put options, contingent
liabilities are implicit put
options, equity and junior claims
are implicit call options
Equity
Banking/
Financial
Sector
Assets
Foreign Def-free
Debt Value – Put
Option
Deposits
and Debt
Value –
Put
Option
See Annex
Contingent Liab
Implicit Put Option
42
Economy-wide Interlinked CCA Balance Sheets with
Assets, Junior Claims, Risky Debt and Cont. Liabilities
Corp
Asset
AC
Households
AFIN
Financial
AF
 AL
Sovereign
Foreign
RFX
 AG
 ( AH , RE
 AS ,Other
 BH , RE
PH , RE )
Cont.
A&L
Equity/
Jr. &
Sub.
Claims
Barrier
EL
(Put )
Sum
 EC
 EH
 PF
 PF
 EF
 M BM
 cD
 BSLC
 PSLC
 BC
 BF
 BSFX
 PC
(1   G ) PF
 PSFX
0
0
0
0
Foreign
Claims
0
43
A=Assets, E=Jr. Claim, B=Def-free Debt, P=Put Options
Economy-wide CCA Balance Sheet Models
Capture Non-linear Risk Transmission

Note that if asset volatility in CCA sector
balance sheets is set to zero:
– Implicit put options go to zero,
– Macroeconomic accounting balance sheets and
traditional flow-of-funds are the result
– Measurement of (non-linear) risk transmission is not
possible using macroeconomic flow or accounting
frameworks

Interlinked implicit options result in
compound options that exhibit highly nonlinear risk transmission, as seen a variety
of financial crises
44
Summary use CCA models of the Financial Sector and
links to Macro Models

Decomposing factors driving bank CDS spreads
– Leverage, asset volatility, Global market risk appetite, loss
given default
– Implicit put options





Vulnerability and stress-testing
Linking credit risk indicators to macro models. Factor models
of CCA asset and risk indicators for systemic stress testing
and link to GDP growth
FX reserves “adequacy” for banking sector contingent
liquidity and credit risks
Integrating financial sector with monetary policy models
Analysis of non-linear risk transmission between key sectors
in an economy-wide CCA balance sheet model
45
Thank you,
More information see:
Papers by D. Gray, Robert C. Merton, Zvi Bodie:

NBER 12637 (2006)

NBER 13607 (2007)

Sovereign Credit Risk, JOIM v. 5, no. 4, Dec 2007

CCA and the Subprime Crisis (Gray, Merton, Bodie forthcoming)
IMF Working Papers: WP 05/155, 04/121, 07/233, Indonesia SIP
(2006), Gray and Walsh (WP 08/89), Gray, Lim, Loukoianova,
Malone (WP/08), IMF Staff Papers Gapen et. al v 55 #1 2008;
Framework for Integrating Macroeconomics and Financial Sector
Analysis by Gray, Karam, Malone, N’Diaye (forthcoming)
Macrofinancial Risk Analysis, Gray and Malone (Wiley Finance book
Foreword by Robert Merton)
202-623-6858
[email protected]
46
Annex 1 - CCA Risk Indicators and Values
Value of Risky Debt, D (B=distress barrier,
P=implicit put option)
D  Be  rt  P  Be  rt  ( Be  rt N (d 2 )  A0 N (d1 ))
 A2 
 A0  
ln     rf 
t
B
2

D-to-D= d    
2
A t
d1  d2   A t
Default Probability
Risk Neutral DP
N (d 2 )
Estimated Actual DP
 A  rf
d  d2 
A
*
2
N (d2* )  N (d2   t )
t   t   Asset , Mkt SharpeRatioMkt t
Credit Spreads
sSrDebt
PBSr 
1 
  ln 1 

t  BSr e rt 
47
Annex 2 - Sovereign, Bank, and Corporate Economywide CCA Sector Interlinked Balance Sheets
Risky Debt = Default-free Value of
Debt minus Expected Losses
Equity
Corporate
Sector
Assets
Default-free
Debt Value
– Put
Option
Money &
Sovereign
Assets
Local
Currency Debt
Expected losses in risky debt are
implicit put options, contingent
liabilities are implicit put
options, equity and junior claims
are implicit call options
Equity
Banking/
Financial
Sector
Assets
Foreign Def-free
Debt Value – Put
Option
Deposits
and Debt
Value –
Put
Option
See Annex
Contingent Liab
Implicit Put Option
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Annex 4 – Aggregation of Credit Risk Indicators (CRIs)
Tractable measures of system risk for use with
macroeconomic models and for financial stability analysis
the CCA credit risk indicators are:
Weight the EDF or distance-to-distress for each institution by
the implied assets of each bank/financial institution to get
a system risk indicator.
Use the median or 75% quartile EDF for the sub-sector or
group, e.g. as calculated by MKMV.
Composite spread or default probability for financial sector,
corporate sector and households (if data is available).
Weight of the volatility and/or skew from put option on
equity of key financial institutions by the assets of the
institution.
Calculate an Nth to default indicator.Calculate the joint
distribution of default probabilities in a portfolio of
financial institutions. Tail risk dependence measure from
equity options or implied assets is another indicator.
49