A Framework for Conceptualizing, Representing, and Analyzing
New Framework for Analyzing Macrofinancial Risk and ...
Transcript of New Framework for Analyzing Macrofinancial Risk and ...
New Framework for Analyzing Macrofinancial Risk and Financial
Stability: Contingent Claims Approach
Presentation at the Bank of Thailand
October 6, 2009
Dale Gray
Sr. Risk Expert
Monetary and Capital Markets Department
International Monetary Fund
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. The presenter’s email is [email protected]
2
Macrofinancial Risk Linkages
Macroeconomic
Models
Monetary Policy
Models
Risk-Adjusted
Balance Sheet Models
(Corporate, Financial,
and Sovereign Sectors)
3
Macrofinancial Risk Analysis
� Framework integrates risk-
adjusted balance sheets
using Contingent Claims
Analysis (CCA) of financial
institutions, corporates,
and sovereigns together
and with macroeconomic
and monetary policy
models
� TOOLKIT FOR MACRO RISK
ANALYSIS
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Outline
I Risk-Adjusted Balance Sheets: The Contingent Claims Analysis (CCA) Framework
• Economy-wide Interlinked Balance Sheets
• Towards Unified Framework for Policy
II Application of CCA to Corporates and Financial Institutions
• Default Probability;
• Stress Testing; Capital Adequacy
• Systemic Risk Analysis
• Impact of Financial Guarantees on Banks and Sovereign Risk
• Integrating CCA Models into Monetary Policy Models
5
Part I Risk-Adjusted Balance Sheets: The
Contingent Claims Analysis (CCA)
Framework
6
Core Concept: Merton Model (CCA) for Firms and Banks
Assets = Equity + Risky Debt
= Equity + PV of Debt Payments – Expected Loss due to Default
Assets
Equity or Jr Claims
Risky Debt
• Value of liabilities derived from value of assets
• Uncertainty in asset value
Note: Measured using option valuation formulas
7
CCA Credit Risk Measures
Asset Value
Exp. asset Distribution of Asset Valuevalue path
Distress Barrier or promised payments
V 0
Time
Probability of Default
T
Distance toDistress: standard
deviations asset value is from debt distress
barrier
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Example for a Thai Corporate
If Assets, at time 0, = 250 bn baht
Volatility of Asset return =15% (annual)
Promised payments on debt = 100 bn baht
This gives:
Default Probability is 0.2% over one year and associated rating is A+
But assets and asset volatility can’t be observed directly: How can they be calculated?
9
Estimating CCA Risk-adjusted Balance Sheets for Financial Institutions and Corporates
If equity is traded in the market, CCA uses forward-looking equity information plus balance sheet data
– Inputs:
• Value and Volatility of Market Capitalization
• Debt Distress Barrier (PV of promised debt payments, from book value)
– Outputs:
• Implied Market Value of Assets and Asset Volatility,
• Default Probability, Expected Losses due to Default, Credit Spread and other Risk Indicators
If there is not traded equity, direct estimation of assets and asset volatility can be used instead
10
Calibrate (Unobservable) Market Value of Asset and Implied Asset Volatility
INPUTS
� Value and Volatility of Market Capitalization, E
� Debt Distress Barrier B (from Book Value)
� Time Horizon
USING TWO EQUATIONS WITH TWO UNKNOWNS
Gives:
Implied Market Value of Assets
and
Asset Volatility
Default Probabilities
Spreads, Risk Indicators
11
Macrofinancial Risk Analysis is Applied at Bank, Sector, and Economy-wide Levels
CCA risk analysis tools can be applied to
measure, analyze and manage risk for:
(i) Financial sector
- Individual Institutions
- System of Institutions
(ii) Corporates and Corporate Sectors
(ii) Sovereigns
(iv) Households
(v) Economy-wide Risk Framework
12
Sovereign, Bank, and Corporate and Household
Economy-wide CCA Sector Interlinked Balance Sheets
Corporate and Household Sector
Assets
Sovereign
Assets
Equity/NW
Default-free Debt Value
– Put Option
Money &
Local Currency Debt
Foreign Def-free Debt Value – Put Option
Banking/ Financial
Sector Assets
Deposits and Debt Value –Put Option
Equity
Contingent Liab
Risky Debt = Default-free Value of
Debt minus Expected Losses
Expected losses in risky debt are
implicit put options, contingent
liabilities are implicit put
options, equity and junior claims
are implicit call options
Implicit Put Option
13
CCA Balance Sheet Models Capture Non-linear Risk Transmission
� Note that if asset volatility in CCA balance
sheets is set to zero:
– All 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 flow-of-funds or accounting
frameworks
� Traditional macroeconomic accounts do
not include risk!
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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
macrofinancial linkages
� Time pattern of CCA risk indicators can be linked
to macroeconomic variables and to monetary
policy models
15
Added Dimension of Risk Indicators CCA Risk Analytics Models to Spectrum of Macroeconomic Models
Risk Analytics Models CCA, Credit Risk Macroeconomic Theory Based RBC, GE IS-LM DSGE, MPM VAR Data Based Macroeconomic Models
16
Where we ultimately want to go…….
Unified Macrofinancial Policy Framework
� Financial Stability Policies
� Monetary Policy
� Fiscal, Reserve and Debt Management
Policies
17
Unified Macrofinance Framework Targets: Inflation, GDP,
Financial System Credit Risk, Sovereign Credit Risk
Sovereign CCA Balance
Sheet Model
Monetary Policy Model
Interest Rate Term Structure
Financial System Credit Risk IndicatorFinancial
Sector CCA Model
• Fiscal Policy
• Debt Management
• Reserve Management
• Policy Rate
• Liquidity Facilities
• Quantitative Actions
• Capital Adequacy
• Financial Regulations
• Economic Capital
Fiscal and Debt Policies:
Guarantees
Financial Stability Policies:
Sovereign Credit Risk Indicator
Monetary Policies:
Household CCA
Balance Sheet(s)
Corporate Sector CCA Balance Sheet(s)
Sovereign Equity Claims (from Capital Injections)
Global Market Claims on
Sovereign
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Traditional Flow and Accounting Framework No Risk-Adjusted Balance Sheets (Asset Volatility = 0)
No Credit Risk or Guarantees; No Risk Exposures
GovernmentAccounts Flow of Funds
Monetary Policy Model
Interest Rates
Bank Accounting Balance Sheets
• Fiscal Policy
• Debt Management
• Reserve Management
• Policy Rate
• Liquidity Facilities
• Quantitative Actions
• Capital Adequacy
• Financial Regulations
Fiscal and Debt Policies:
Financial Stability Policies: Monetary Policies:
Household AccountingBalance Sheet(s)
Corporate AccountingBalance Sheet(s)
Capital Injections
Global Market Flows
Credit Flows
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Part II Application of CCA to Corporates
Financial Institutions and Systemic Risk
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II. Application of CCA to Corporates and Financial Institutions
Examples for Two Thai Corporates (Moody’sKMV Model)
Large Thai Corporate
Asset 246 bn baht
Asset volatility 14 %
Default barrier 102 bn baht
Default Prob (EDF) 0.15%
Credit Spread 265 bps
Small Thai Corporate
0.35 bn baht
50 %
0.14 bn baht
4.2 %
1320 bps
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Median (50th Percentile) Corporate Sector Default Probability for the last 2 years (up to Oct 1, 2009)
0
2
4
6
8
10
129/
30/2
007
10/3
0/20
07
11/3
0/20
07
12/3
0/20
07
1/30
/200
8
2/29
/200
8
3/30
/200
8
4/30
/200
8
5/30
/200
8
6/30
/200
8
7/30
/200
8
8/30
/200
8
9/30
/200
8
10/3
0/20
08
11/3
0/20
08
12/3
0/20
08
1/30
/200
9
2/28
/200
9
3/30
/200
9
4/30
/200
9
5/30
/200
9
6/30
/200
9
7/30
/200
9
8/30
/200
9
9/30
/200
9
One
Yea
r D
efau
lt P
roba
bilit
y in
Per
cent
...
THAILAND CORPORATES GROUP
INDIA CORPORATES GROUP
MALAYSIA CORPORATES GROUP
HONG KONG CORPORATES GROUP
JAPAN CORPORATES GROUP
US CORPORATES GROUP
SINGAPORE CORPORATES GROUP
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50
55
60
65
70
75
80
85
90
95
100
0 5 10 15 20 25 30 35
1-year EDF (%)
Per
cent
age
of C
umul
ativ
e A
sset
s
1/9/2007
9/1/2008
3/18/2009
Thailand Corporate Sector – Cumulative Assets vs
Default Probability
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CCA Model for Banks
Examples for Two Groups of Thai Banks (Moody’sKMV Model)
Large Banks (average)
Asset 1200 bn baht
Asset volatility 3.9 %
Market Cap 180 bn baht
Default barrier 914 bn baht
Default Prob (EDF) 0.1%
Credit Spread 110 bps
Small Banks (average)
120 bn baht
6.7 %
11.5 bn baht
96 bn baht
0.75 %
340 bps
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50th Percentile Default Probability for Banking Groups for the last 2 years (up to Oct 1, 2009)
0
1
2
3
4
5
6
7
9/30
/200
7
10/3
0/20
07
11/3
0/20
07
12/3
0/20
07
1/30
/200
8
2/29
/200
8
3/30
/200
8
4/30
/200
8
5/30
/200
8
6/30
/200
8
7/30
/200
8
8/30
/200
8
9/30
/200
8
10/3
0/20
08
11/3
0/20
08
12/3
0/20
08
1/30
/200
9
2/28
/200
9
3/30
/200
9
4/30
/200
9
5/30
/200
9
6/30
/200
9
7/30
/200
9
8/30
/200
9
9/30
/200
9
One
Yea
r D
efau
lt P
roba
bilit
y, P
erce
nt.
THAILAND BANKS GROUP
INDIA BANKS GROUP
MALAYSIA BANKS GROUP
JAPAN BANKS GROUP
UNITED STATES BANKS GROUP
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0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Apr-09 Jul-09
Ratio of Implied Market Value of Assets to Liabilities for Example Banks
Default zoneLehman
JPMorgan
Citigroup
26
CCA Models are useful because they:
� measure credit (default) risk
� link equity value and volatility to credit
spreads
� CCA is useful not just to analyze default
risk, but risk of declining below any
barrier, e.g. minimum capital /prompt
corrective action barrier for banks, or
risk of declining from AA rating to BBB
rating, etc.
27
Some Applications of CCA models:
Stress-testing with CCA plus Factor Model
Quantitative assessment the impact of government interventions and unwinding (capital adequacty debt and asset guarantees, etc.)
“Systemic CCA” used to determine systemic tail-risk in the banking system and government contingent liabilities.
Risk transfer from financial sector to the sovereign
Integrating financial sector into monetary policy models
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EXAMPLE: Bank-by-Bank CCA and Factor Models for Stress-Testing
Procedure:
� 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 Step 2 Step 3 Step 4
Scenario generation (global and domestic factors)
Factor Model for bank asset return (or bank risk indicators)
CCA model for each bank (or bank group)
Impact on bank credit risk, (POD, implicit put, spread) and on equity capital
Gray, D. and J. Walsh (2007) “Factor Model for Stress-testing
with a Contingent Claims Model of the Chilean Banking
System.” IMF Working Paper 08/89.
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EXAMPLE OF CHILE BANK FACTOR MODEL - Banks have Heterogeneous Response to Individual Factors; Stress testing canbe with individual factors or with Four Principal Components
Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6
VIX Chile CPI IMACEC Chile Unemp.S&P Yld Curve 10-Yr (Chg) Oil Chile CPI CLP / BRLIPSA 1-Yr (Lvl) 1-Yr (Chg) Copper Copper
CLP / USD US CPI
Financials Cyclicals Domestic Domestic/(Levels) Change Regional
U.S. Rates
U.S. Rates
Factors associated with different components of asset returns
Factor 1 Factor 2 Factor 3 Factor 4
0%
1%
2%
3%
4%
5%
6%
7%
1 4 7 10 13 16
Scenario 1: Shock to Financials Variable Comparable to 2003
Defau
lt Pro
bability
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Key Points on Using CCA for Policy
� CCA + Factor Model provides “CCA Early Warning Stress Testing System”
� CCA + VAR models can capture macroeconomic, corporate and banking sector feedback effects
� Useful for Economic Capital Adequacy CCA can be used to measure cost and benefits of:
– Financial guarantees and deposit insurance (can be used to estimate the proper guarantee fee to be charged)
– Risk transfer to sovereign
– Combinations of policies (capital adequacy, liability guarantees, asset guarantees, other)
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Tradeoffs between Market Capitalization, Market Value of Assets and Default Probability
Citigroup Example: From Sept 9, 2008 to March 9, 2009, Market Capitalization fell from $125 bn to $6, Assets declined and Default Probability went from 0.5% to 24%
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
1,400,0001,500,0001,600,0001,700,0001,800,0001,900,0002,000,0002,100,000
Market Value of Assets (million $)
Mar
ket C
apita
lizat
ion
(mill
ion
$)0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
0 5 10 15 20 25 30
EDF, One Year Default Probability in PercentM
arke
t Cap
italiz
atio
n (m
illio
n $)
Changes in market cap (common equity) affect
default in a non-linear way
32
In April 2009, Possible Strategies to get to Citigroup to a Target Default Probability of say 0.3% (=BBB+ rating)
Option 1 – Capital Injection: Increase market
capitalization by $ 99 bn
Option 2 – Asset Purchase and/or Ring-fenced
Asset Guarantee which lowers asset volatility
by 10% plus increase market capitalization
by $65 bn
Option 3 – Reduce short-term liabilities by
$140 bn (voluntary debt for equity swap)
plus reduce volatility by 10% plus increase in
capital by $18 bn
33
After Stress-tests Citigroup raised common equity (market cap) back to up to $107 bn
Default probability went from 25% down to 0.3% by Sept 2009
0
20000
40000
60000
80000
100000
120000
140000
1,400,0001,600,0001,800,0002,000,0002,200,000
Market Value of Assets (million $)M
arke
t Cap
italiz
atio
n
0
20000
40000
60000
80000
100000
120000
140000
0 5 10 15 20 25 30
EDF One Year Default Probabilitiy Percent
Mar
ket C
ap
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Systemic CCA
Systemic risk is ultimately about fiscal liabilities
But market-based indicators net out guarantees (or cost expected to be borne by government)
Here, computing implicit put options (expected losses) from equity markets (rather than debt markets) to split risk borne by government vs. risk retained by banks
(preliminary results for US from Gray and Jobst, 2009)
35
Implied CDS spreads are much higher than observed CDS spreads, which are net of government liability guarantees
(Gray, Merton, Bodie 2008 and Gray and Jobst 2009)
Government contingent liability = αααα*implicit put option derived from bank equity
Value of put option on CDSα = 1 -
Value of put option on equity
Assets = Implicit Call Option + [Default-Free Debt – (1-
α)*Implicit Put Option] – α*Implicit Put Option
Using CCA with equity information and information
from CDS spreads allows us to calculate the share
of risk born by the government
36
Systemic CCA
Multivariate extreme value dependence model is then used to calculate the multivariate density and thus the government’s contingent liabilities accounting for the time-varying and non-linear dependence (correlation)
37
US Systemic CCA Model (preliminary analysis)Simple Sum of Contingent Liabilities to Banks (gray area) vs50th Percentile from Multivariate Distribuiton(Jobst, 2009, Gray and Jobst 2009)
US Financial Sector Systemtic CCA - Simple Sum of Contingent Liabilities vs 50th Percentile of Multivariate
Density of Contingent Liabilities 1/
0
500
1,000
1,500
2,000
2,500
26-Jun-
08
10-Jul-
08
24-Jul-
08
07-Aug-
08
21-Aug-
08
04-Sep-
08
18-Sep-
08
02-Oct-
08
16-Oct-
08
30-Oct-
08
13-Nov-
08
27-Nov-
08
11-Dec-
08
25-Dec-
08
08-Jan-
09
22-Jan-
09
05-Feb-
09
19-Feb-
09
05-Mar-
09
19-Mar-
09
02-Apr-
09
16-Apr-
09
30-Apr-
09
14-May-
09
28-May-
09
In U
S d
oll
ar
bil
lio
ns
Total Contingent Liabilities (simple summation of avg. individual contingent liabilities)
Total Contingent Liabilities (average univariate marginals, GEV, 50th percentile)
Sample period: 06/26/2008-06/10/2009 (271 obs.) of individual contingent liabilities of sample banks. Source: IMF staff estimates. 1/ The multivariate density is generated from univariate marginals that conform to the Generalized
Extreme Value Distribution (GEV), estimated via the Linear Ratio of Spacings (LRS) method over an estimation window of 30 days, and a non-parametric identification of the time-varying dependence structure.
38
Example of Systemic CCA Applied to Group of Banks Country to Analyze Systemic Tail-Risk (preliminary analysis)
Contribution banks identified as needing more capital (red) to
multivariate contingent liabilities of US government at the 99th
percentile and those banks not needing more capital (green)
39
Estimation of Government Contingent Liabilities
Explicit or implicit government guarantees
mean the government is taking over part of
the banks’ Expected Loss due to Default
Assets =
Equity + PV of Debt Payments – Expected Loss due to Default
Government’s share of Expected Loss due to Default are the Government’s contingent liabilities
40
Risk Transfer to Sovereign Balance Sheet
� Financial Guarantees Raise Expectation of
Higher Fiscal Costs which Reduces Sovereign
Assets, can increase Sovereign Spreads
� Sovereign CCA Model*:
ASov = Reserves + PV (primary fiscal surplus)
+ Other – Contingent Liabilities
*See JOIM paper December 2007 (Gray, Merton, Bodie) and IMF Staff Papers March 2008
41
Ireland Example is Dramatic – After Bank Debt Guarantees, Bank CDS decreases and sovereign CDS increases.
0
50
100
150
200
250
300
350
400
1 21 41 61 81 101 121 1410
50
100
150
200
250
300
350
400
Allied Irish Bank
Bank of Ireland
Sovereign
42
20
40
60
80
100
120
140
160
180
Jul-08 Oct-08 Jan-09 Apr-09
0.0%
0.1%
0.2%
0.3%
0.4%
0.5%
Higher Contingent Liabilities Can Increase Sovereign Risk
Country Example: contingent liabilities are correlated and lead the sovereign default probability (inferred from sovereign CDS
spreads)
Total contingent liabilities(LHS, US$bn)
Est. sovereign default prob. 1-year(RHS, %)
43
Incorporating Financial Sector Risk into Monetary Policy Models
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.
� Explicit inclusion of CCA systemic credit risk/financial fragility indicator captures financial accelerator and crisis periods.
44
How can a system financial fragility indicator be included in monetary policy models?
– In the GDP Output Gap equation
45
Chilean Example – CCA banking system risk indicator is related to Output and Output Gap
-6
-4
-2
0
2
4
6
8
10
12
Jun-97 Jun-00 Jun-03 Jun-06
DTD of Banking System
Output Annual Growth
Output Gap
Distance to Distress (DTD) for the Chilean Banking System, Output and Output Gap
-6
-4
-2
0
2
4
6
8
10
12
Jun-97 Jun-00 Jun-03 Jun-06
DTD of Banking System
Output Annual Growth
Output Gap
DTD has significant and positive
impact on output gap
46
Monetary Policy + CCA Model
Uses a simple two-module framework:
1. Macro Monetary Policy Model.
2. CCA Financial System Module.
This macro model includes the financial stability/ credit risk indicator (banking system distance to distress) in the output gap equation and the exchange rate equations.
47
What happens if Interest Rates react to the
banking sector fragility indicator: Including
DTD in the policy rule reduces inflation
volatility and output volatility
The size of the reaction to DTD in the Taylor rule has a very significant effect on the
results. Indeed The larger the coefficient associated to DTD in the authorities
reaction function, the closer to the origin is the frontier obtained with the
simulations (orange line in Figure below).
Base model reaction to dtd: 0.5, 1.0 ,1.5
2.0
3.0
4.0
5.0
6.0
3.0 4.0 5.0 6.0 7.0
Inflation volatility
Out
put v
olat
ility
DTD: 0.5
DTD: 1.0
DTD: 1.5
48
Summary
CCA incorporates risk-adjusted balance sheets and credit risk into macro and financial stability analysis
Numerous Applications, such as:
� Early warning
� Stress testing
� Assessing quantitative impact of capital raising and government policy interventions in the financial system
� Systemic CCA calculates contribution of banks to tail risk and can be used to set systemic risk charges
� Analysis of risk transfer to the sovereign
� Model for including financial sector risk in monetary policy models
49
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
� HBS WP 09/015 August 2008
� CCA and the Subprime Crisis (Gray, Merton, Bodie) found at:
www.greta.it/credit/credit2008/Tuesday/06_Bodie_Gray_Merton.pdf
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;
Macrofinancial Risk Analysis, Gray and Malone (Wiley Finance book Foreword by Robert Merton)
Annual Review of Financial Economics 2009 “Modeling Financial Crises and Sovereign Risk” by Dale Gray
202-623-6858 [email protected]
50
Parallels between Explicit and Implicit Option Prices
A=E+B-ELS=C+K-PNote put call
parity relation
Expected credit
loss on debt (EL)
Explicit put
option value (P)Put Option
Equity or junior
claim (E)
Explicit call
option value (C)Call Option
Debt distress
barrier (B)
Strike price of
option (K)Strike Price
Asset on balance
sheet (A)
“Asset” such as
stock price, FX,
etc. (S)
Underlying
“Asset”
CCA Implicit
Option Prices
Explicit
Option Prices
51
Simplest Description of Option Values with a “Stochastic or Uncertain” Asset
Assets = max (A-B,0)
Be-rt - max(B-A,0)
Call Option = Equity = max (A-B,0)
Risky Debt =Be-rt - max(B-A,0)
Put Option = max(B-A,0)
(Note, if the asset A is not stochastic, i.e. it has no volatility,
then in a balance sheet context, the put option goes to
zero and the call option turns into the “accounting balance
sheet” or “net worth balance sheet”)