Risk Measurement
Risk Architecture
and the
Bank of the Future
Ron Dembo
Know Your Risk
Founding Chairman
Algorithmics Incorporated
May, 2004
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©2003 Algorithmics Inc.
Overview
1. Measuring Risk: The scale of the problem
2. State of the Market
3. Risk Architecture
4. Simulation, Static and Dynamic (Mark-to-Future)
5. Optimization
6. Potential topics for research
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©2003 Algorithmics Inc.
Open Research
1. Scenario Generation
2. Portfolio Compression
3. Pricing in Illiquid Markets
4. Near-Time Risk for a Large Institution
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©2003 Algorithmics Inc.
Measuring
Risk
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©2003 Algorithmics Inc.
A Portfolio in the Future
Distribution (tn) = F {price, yields ( many currencies), correlations,
Frequency
growth rates, exchange rates, volatility surfaces, etc.}
0
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©2003 Algorithmics Inc.
Derivatives
“Weapons of mass destruction”
“The only thing
we understand
is that we don’t
understand how
much risk the
institution is
running.”
Warren Buffet
Fortune, March 17, 2003
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©2003 Algorithmics Inc.
Know your Risk
Enron
“…..we have a liability of 350 million due April……”
or………
….we have a liability of 350 million due April…..
….drop 2 notches is credit rating and this becomes
9 Billion!
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©2003 Algorithmics Inc.
Know your Risk
JP Morgan (Enron)
Day 1:
Exposure = $500 Million
Day 5:
Exposure = $1
Day 12:
Exposure = $1.9 Billion
Billion
What is the real exposure?
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©2003 Algorithmics Inc.
Know your Risk
Nortel
Largest company in Canada by Market Cap (= Mutual Funds)
30% drop in a day!
> 10 Billion Market Loss
Compensation Risk!
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©2003 Algorithmics Inc.
Know your Risk
HSBC
One of the largest banks in the world
> 60 trading floors
> 90 countries
> 4000 traders
> 300 “Enron” sized counterparties
Each with many subsidiaries, trading with any part of the bank
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©2003 Algorithmics Inc.
“Simple” Questions
What is my exposure,
expected loss and
regulatory capital
for United Airlines ?
What is my exposure
And regulatory capital
associated with Brazil ?
What is my total
Capital requirement
for the bank ?
Corporate group
Division
Risk
Taker
What is
my exposure and
regulatory capital to
non-investment
grade products ?
What is my
regulatory capital
against tech sector
for our Asian sub ?
Subsidiary
What is my
economic capital
for North American
subsidiary ?
Branch
What is my
regulatory capital
on retail mortgages
for UK division ?
Product
Set
Risk
On
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©2003 Algorithmics Inc.
Coherent Measures & Credit Risk
Single Corporate 8% zero bond, 1 year maturity
Payoff (1 year):
$108
$ 54
99.89%
..
(no default)
0.11% (default)
VaR (99%) = $ 0.00
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©2003 Algorithmics Inc.
Coherent Measures & Credit Risk
Portfolio of 10 independent bonds same characteristics
Payoff (1 year): $108 / 10
$ 54 / 10
VaR (99%) = $ 5.40
98.9%
..
1.1%
(no default)
(default)
More diversified ====> More Risk ???
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Risk and Return
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©2003 Algorithmics Inc.
At the end of the day….
Mark-to-Future
+
+
Upside
+
Mark-to-Market
Downside
-
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©2003 Algorithmics Inc.
Simulation (the Upside)
The Horizon
+
+
Max{0, (Mx - eq´x)}
+
+
The Upside has the payoff of a Call option on net exposure !
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©2003 Algorithmics Inc.
Simulation (the
Downside)
The Horizon
Max{0, -(Mx - eq´x)}
-
-
The Downside is a Put option on net exposure !
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Decomposing a Risky
Decision
Call
(Mx - eq´x)+
Put
(Mx - eq´x)-
Inherently forward-looking !
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Risk-Adjusted Performance
Regret
+
+
-
Upside - l Downside
(Call)
(Put)
(Equity)
(Debt)
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The “Put / Call” Efficient Frontier
Maximize: Upside Subject to:
Limited Downside
Call
Put
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Risk-Adjusted Performance
+
+
-
Call - l Put
l>1
Concave function of
net exposure
Exposure
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©2003 Algorithmics Inc.
The “Put / Call” Efficient Frontier
Max:
p´u
Subject to:
p´d  k
where:
u - d - (Mx -rq´x) = 0
()
( )
u  0; d  0
u´d = 0
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©2003 Algorithmics Inc.
Dual of “Put / Call” Trade-off
Max:
p´u
Subject to:
p´d  k
()
where:
u - d - (M - rq´)x = 0
()
u  0; d  0
Min:
kµ
Subject to:
(M - rq´)´ = 0
(x)
p   - µp  0
(u,d)
µ0
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©2003 Algorithmics Inc.
Dual of “Put / Call” Trade-off
Min:
kµ
Subject to:
(M - rq´)´ = 0
(x)
p   - µp  0
(u,d)
µ0
+
(/)
+
Dual feasibility (r = 1) implies:
+
M´(/) = q
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©2003 Algorithmics Inc.
Complementarity
Max:
p´u
Subject to:
p´d  k
()
where:
u - d - (M - rq´)x = 0
( )
u  0; d  0
Min:
kµ
Subject to:
(M - rq´)´ = 0
(x)
p   - µp  0
(u,d)
µ0
´{u - d - (M - rq´)x} = 0
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©2003 Algorithmics Inc.
Complementarity
´{u - d - (M - rq´)x} = 0
(/)´u - (/)´d = (/)´(Mx - q´x)
Call -
Put
=
Future Gain/Loss
Complementarity iff Put / Call parity !
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©2003 Algorithmics Inc.
Modelling Liquidity
Price vs. Quantity is piecewise linear
x = x1 + x2 + x3
(x1)L  x1  (x1 )U
Price
0  x2  (x2)U
0  x3  (x3)U
“fill” (x1)
before (x2)
Quantity
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before (x3)
©2003 Algorithmics Inc.
The Put/Call Efficient Frontier
k (  > 1; infinite liquidity )
Call(k)
k - (wU) xU + (wL) xL
Adjustment for liquidity
k
(Put)
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Prices in an Illiquid Market
Different tolerances for downside lead to different risk neutral discount
factors
Call
r3
r2
Put
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Replication
0
Target
0
Portfolio
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Single Period, Multi State
Probabilities
1
m11
m21
m31
t1
m12
m22
m32
t2
m13
m23
m33
t3
Security Prices
q1
q2
q3
2
c
3
portfolio
benchmark
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State Values
©2003 Algorithmics Inc.
“Regret” Based Efficient Frontier
MR(K) = Minimize x ..... E ( ||(MTx - t)||- )
Subject to :
Regret
[E {MTx} -qTx] - [ E {t} - c] > K
portfolio gain
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-
target gain
©2003 Algorithmics Inc.
A “Nobel” Quote
“…I should have computed the historical covariance of the asset
classes and drawn an efficient frontier….Instead I visualized my
grief if the stock market went way up and I wasn’t in it…or if it
went way down and I was completely in it. My intention was to
minimize my future regret, so I split my contributions 50/50
between bonds and equities..”
Harry Markowitz
(Money Magazine 1997)
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©2003 Algorithmics Inc.
Images of a Portfolio
Inverse problems
p1
p2
p3

Implied Views

Stability of Optimal solutions

No-arbitrage (risk-neutral)
parameters (implied discount
factors, distributions)
0
Portfolio
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©2003 Algorithmics Inc.
Immunization
US Govt. Bond Portfolio
Ranges
Govt. Book
Scenario Opt. Hedge
PV01 Hedge
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©2003 Algorithmics Inc.
Immunization
99% Confidence VaR
US Govt Book
$6,480,000
.. With PV01 Hedge
$2,275,344
.. With Scenario-Optimal Hedge
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$353,634
©2003 Algorithmics Inc.
Portfolio Compression
Portfolio:
1,025 Positions
Composition:
Options on Bond Futures
4.9%
Callable Bonds
4.8%
Caps/Floors
32.3%
Bond Futures
1.6%
Interest Rate Swaps
15.5%
Treasury Bills, Bonds, Strips
40.9%
Replication with hypothetical Treasury Strips, European Options on longdated Treasury Bonds, spanning monthly periods from January 1995 to
December 2025
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©2003 Algorithmics Inc.
Compressed Portfolio
Compressed Portfolio: 51 Positions (simple)
Scenario Set:
50 randomly generated
Composition:
17 puts on long-dated Treasury Bonds
32 calls on long-dated Treasury Bonds
2 Treasury Strips
Replication with hypothetical Treasury Strips, European Options on longdated Treasury Bonds, spanning monthly periods from January 1995 to
December 2025
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©2003 Algorithmics Inc.
Compression Results
VaR Original (95%)
VaR Compressed (95%)
14,963,188
14,981,115
Error < 5 basis points!
TIME ( Compressed )
TIME ( Original)
<
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1 / 1000
©2003 Algorithmics Inc.
Risk
Architecture
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©2003 Algorithmics Inc.
Risk Computation Needs
Overnight
Intraday
Real-time
A single risk architecture must be able to handle business
needs ranging from overnight batch to real-time
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©2003 Algorithmics Inc.
Risk Computation Needs
e.g. Counterparty credit exposures
Overnight
Intraday
Baseline exposure profile
Real-time
Pre-deal checking
“Round robin” 24x7 updating
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©2003 Algorithmics Inc.
Risk Architecture
Monolithic
vs
Distributed
Intraday possible
Inherently slow
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Distributed Architecture
Multiple data sources
communicating with multiple risk engines
producing output in multiple locations
all interconnected !
Data
Risk Engines
Output
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Mark-to-Future
An Architectural Vision
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©2003 Algorithmics Inc.
Mark-to Future
Scenario based
Links all risk types
Full forward valuation,
no shortcuts
Separates simulation
and reporting
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©2003 Algorithmics Inc.
An example of the complexities
The floating leg of a swap:
value
date
now
Bond
age
Bond
age
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An example of the complexities
The floating leg of a swap:
value
date
now
…
reset date
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The “Cube”
The Mark-to-Future “Cube”
Scenario
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MtF of a Portfolio
3
Scenarios
5
16
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All Instruments
Any
(MtF)
Portfolio
MtF
sort
statistics
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MtFCube
Mapping
Scenarios
Netting,
Credit Mitigation
Collateral, etc.
Mark-to-Future
Mark-to-Future
Mark-to-Future
Instruments
Values
Credit Portfolio
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©2003 Algorithmics Inc.
Mapping to Basis Instruments
Product
Basic Instrument
Risk Factor
3M Zero
6M Zero
1Y Zero
5Y Zero
3 month rate
6 month rate
1 year rate
5 year rate
e.g.
Bond
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Maps for Equities
MtM
Scenarios
f11 + f2 2 + f33
MtF
m11 
1
m11 2
m11 3
d1
m21
m21
m21
d2
m31
+
m31
+
m31
=
d3
Stock or portfolio of stocks
Is mapped into
Factor MtF (done once!)
a portfolio of factors
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©2003 Algorithmics Inc.
A Swap Portfolio
Single Currency;
40,000 (Vanilla) Swaps
20 points on yield curve; 1000 scenarios; 10 time periods
1000
=
200,000!
Swap Portfolio = F(m1,…,m20 )
Risk in an instant!
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©2003 Algorithmics Inc.
“Real Time” Mark to Future
Counterparty portfolio:
• 2000 positions
• 83 risk factors
• FRAs, FX Forwards & Options, IRS,
Caps/Floors, Swaptions etc… (long & short
positions)
• 1000 scenarios across 50 time steps
• netting agreements & collateral
Pre-deal ‘what-if’ for new interest rate swap with a counterparty:
Total simulation and aggregation time to derive a full montecarlo updated profile:
13 seconds!!!!
Simulation
Heavy
Light
MtF
Incremental Deal
Aggregation
Full MtF
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Exposure Calc
Statistics
©2003 Algorithmics Inc.
Consistency
Consistent Measurement of Earnings and Value at Risk
Scenarios
Growth and
re-investment
assumptions
Earnings-at-Risk
Cash flow
generation
Valuation
Models
Value-at-Risk
Post-cube
Pre-cube
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©2003 Algorithmics Inc.
Mark-to Future
Without the “cube”,
scalability to 20,000
users in real time
would be prohibitive!
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©2003 Algorithmics Inc.
Only a few scenarios are relevant!
Mean of Distribution (10,000 scenarios)
11 “Bucket Scenarios”
reproduce the distribution for
1/1000th the work!
Mean of a Bucket
Single scenario result
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©2003 Algorithmics Inc.
Liquidity and the
true simulation
of dynamic
portfolio risk
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©2003 Algorithmics Inc.
Dynamic Portfolios
Portfolio
changes
Function of the
scenarios and
strategy
Time
Events
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©2003 Algorithmics Inc.
A Regime
A “Regime”
If( margin on the derivatives book is
below s, liquidate sufficient bonds to
raise it to S)
Apply to all marked nodes
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Funding Liquidity Risk
Time
Multiperiod
Simulation
Cash /Collateral
Account
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The Regulators
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Convergence
Regulatory Capital and Economic Capital will converge
Gap Analysis
Duration
Asset Liability
Parallel Shifts
Earnings Simulation
Fair Accounting Value
Management
Integrated
ERM
Market Risk
Management
Scenario Based VaR
Parametric VaR
Stress Tests
Sensitivity
Basel 1
1970 - 1979
1980 - 1989
1990 - 1999
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Basel 2
2000+
©2003 Algorithmics Inc.
State of the Enterprise Risk Market
(Banks) Mapped to Products
Innovators
Early
Adopters
Early
Majority
Late
Majority
Laggards
(Skeptics)
Risk
Architecture
Maturity
Credit risk
Collateral
Market risk
Operational
Risk
Market
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©2003 Algorithmics Inc.
State of the Enterprise Risk Market
(Asset Managers) Mapped to Products
Innovators
Early
Adopters
Risk
Architecture
Early
Majority
Late
Majority
Laggards
(Skeptics)
Market risk
Maturity
Credit risk
Collateral
Operational
Risk
Market
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©2003 Algorithmics Inc.
State of the Enterprise Risk
Market
Mapped to Regulations
Maturity
Innovators
Early
Adopters
Early
Majority
Patriot Act
FSA 195
SarbanesOxley
Late
Majority
Laggards
(Skeptics)
FAS 133
Basel I
Basel II
Market
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©2003 Algorithmics Inc.
The Regulatory Environment
Basel II is a regulatory framework for
risk measurement
•
•
•
Market Risk (as in previous accord)
Credit Risk (a fundamental change)
Operational Risk (new)
Just think back to the fundamental
changes to risk management practice
brought about by Basel I.
Basel II will result in much bigger
changes.
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©2003 Algorithmics Inc.
Use test to qualify for waiver
“institutions wishing to qualify . . . will have to
prove . . .that the internal ratings system and its
component parts are all used in the active day-to-day
granting of credit.”
From the New Basel Accord.
• pricing of credit risk
• incorporation of credit mitigation
• setting of credit limits
• calculation of economic capital
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©2003 Algorithmics Inc.
Basel II Highlights
The biggest change will occur in the measurement and
management of credit:
•
credit touches all aspects of banking
•
significant amount of new sophistication in credit
measurement infrastructure
•
usage criteria will require banks to re-engineer their IT
architecture
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©2003 Algorithmics Inc.
Basel II ..some quotes
“…..Basel II is nice, but we are re-architecting our
credit infrastructure because it is good for
business!”
…Tim Howell, Head Group Treasury, HSBC
In the first day of operation of its new credit risk system,
HSBC saved more than the cost of the software!
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©2003 Algorithmics Inc.
The Bank of the Future
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©2003 Algorithmics Inc.
A Fundamental Change
Today:
Banks do business and then compute risk
Tomorrow:
They will compute risk and then do business!
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©2003 Algorithmics Inc.
Banks Today
(Non-Traded) Products
Traded Products
Capital Mkts
Capital Mkts
Market Risk
Credit Risk
ERM
ERM
Credit Risk
Collateral
Limits
Asset
Credit
Liability
Risk
Limits Mgt.
Limits Mgt.
Limits Mgt.
Limits Mgt.
Front
Front
Front
Front
Retail
Comm.
Credit
Middle
Middle
Middle
Middle
Mortgages
Lending
Cards
Back
Back
Back
Back
Credit
Swaps Derivatives
Fx
Emerging
Markets
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©2003 Algorithmics Inc.
Convergence
Regulatory Capital and Economic Capital will converge
Gap Analysis
Duration
Asset Liability
Parallel Shifts
Earnings Simulation
Fair Accounting Value
Management
Integrated
ERM
Market Risk
Management
Scenario Based VaR
Parametric VaR
Stress Tests
Sensitivity
Basel 1
1970 - 1979
1980 - 1989
1990 - 1999
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Basel 2
2000+
©2003 Algorithmics Inc.
Enterprise Risk Today
Bonds
FX
Swaps
Equity
Banks today are a collection
of Independent silos
Enterprise risk is an adjunct
to the operation (one way)
Bank of today
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©2003 Algorithmics Inc.
A Non-Invasive Architecture
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©2003 Algorithmics Inc.
Bonds
FX
Swaps
Equity
The Bank of the Future
Risk computation will no longer be an adjunct
to the business, it will be at the core
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©2003 Algorithmics Inc.
Vision….usage scenarios
A global investment bank 8 am any day of the week
You are the CFO for the Global Credit Operation and you have just come
into your office to review the P/L statement for your global loan portfolio.
You download a report that has undertaken a full mark-to-market for your
loan book on a daily basis.
Using credit spread curves that are updated daily using the bond and credit
default swap markets along with credit migrations from the day before you
are able to analyze your loan balance sheet on the same basis as your
trading book -- including assessing the embedded optionality such as
prepayment and credit line utilization.
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©2003 Algorithmics Inc.
Conclusions
Today……….. enterprise risk systems are an adjunct to a bank
Tomorrow…... they will be central
Up until today.. risk architecture has not been so important
Tomorrow…… it will separate high performing banks
from under-performers
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©2003 Algorithmics Inc.
The End
Financial Intelligence
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©2003 Algorithmics Inc.