1. Indizen Quantitative Solutions
Corporate
Presentation
Contact details:
paco.sanchez@indizen.com
℡ + 34 615 903 579
1

2. 2
Indizen Technologies
Indizen is a company that specializes in technology
and quantitative analysis. We provide these services
to our clients in three different ways:
We provide our clients with timely access to cost effective,
indizen highly qualified professionals with advanced technological
human
capital and quantitative skills.
We deliver closed projects for our clients. By using our own
indizen development methodology and architecture iMade we
labs
guarantee a prompt and robust delivery.
indizen We offer quantitative models and solutions to help our clients
quantitative make the best business decisions. We have a sound, proven
solutions
experience in the modeling of financial markets and operations.

3. 3
Corporate Principles
• Our employees are our most valuable asset. Their knowledge, experience
and ingenuity are the key factors for the success of our projects.
• We actively encourage our employees to share their ideas, creativity
and skills so that they became part of the global knowledge of the
company.
• We promote innovation and creativity in our work.
• Our relationship with our clients is based in the highest ethical standards
of honesty.
• We develop our work with the highest levels of scientific objectivity in
order to provide tools to make the best business decisions.
• We are committed to using the most appropriate techniques and
technologies for the benefit of our clients.

4. 4
Who we are
Enrique Mota is the CEO of Indizen Technologies and
since the foundation of the company he is
responsible for business development.
He has actively participated in some of our most relevant
R&D&i projects in the health industry, telecom, finance
and energy and he deployed our proprietary
methodology for project development (iMade), which is a
key factor for a successful delivery of our projects by
monitoring the quality of the innovation process.
He is currently focusing on the analysis of the natural language and the ways to
apply semantic models in order organize and classify information according to
different coding international standards. These techniques are applied in different
commercial software packages that we offer to the health care sector.
Quique holds a degree in Telecom Engineering from the University of Alcalá de
Henares (Spain)

5. 5
Who we are
Daniel Crespo is one of the founding partners of
Indizen Technologies. He pioneered the first steps of
the company in the world of the web technologies and
e-business. He has worked in several successful
projects in the financial risks industry and back in
2003 he launched our first project on nuclear risks
with the involvement of the Spanish Nuclear Security
Council.
Since 2005, Daniel is CEO of Indizen Optical
Technologies a spin-off of Indizen and a joint venture with a number of university
professors created to develop optical technologies for different industrial
applications. IOT is currently active in four continents commercializing state-of-
the-art software for ophthalmic lens design, with a rapidly growing portfolio of
clients. Other projects involve development of optical metrology applications for
Airbus and INTA (the Spanish Space Agency).
Daniel holds a Ph.D. in Physics from the Universidad Complutense of Madrid.

6. 6
Who we are
Jesús Gil is an experienced consultant in IT. Previous
to the creation of Indizen Technologies, in which he is one
of the founding partners, he worked as an IT consultant
for large consulting firms as well as for the public
administration. In these activities he acquired extensive
experience in the modeling, design and development of
large systems, and in the management of large teams of
consultants.
He leads complex simulation projects, such as one of
particular interest for the Company related to safety and risks control in nuclear
power plants, currently in use by the Spanish Nuclear Security Council.
Since 2007 Jesús is CEO of Szena Risk, a joint venture with Indizen and a group
of financial consulting experts, aimed at developing software solutions for the
Financial Industry with focus on Risks Management and Pricing Models. Szena
has a portfolio of technological solutions with a presence in major Spanish
financial institutions.
He has a degree in Theoretical Physics from the Universidad Autónoma de
Madrid.

7. 7
Who we are
Alberto Gómez joined Indizen Technologies in 2002. He is
currently the CTO of the firm and manages the Distributed
Systems areas of the company and Financial Projects.
He successfully managed several complex projects for the
main clients of the company in the development of the
market risk management system, the counterparty credit
exposure calculation system at Santander and the
external models valuation system at Caja Madrid.
Before joining Indizen he lead IT projects in different fields such as Terrestrial
Digital TV, Telecommunications and CAD/CAM in engineering and R+D
departments. He has a wide experience in financial risks and grid technologies
and is an expert in software development methodologies and programming
languages.
He has a master degree in Telecommunication Engineering from the Universidad
Politécnica de Madrid, an Executive Master in Financial Risk management and is
certified Financial Risk Manager (FRM) by the Global Association of Risk
Professionals (GARP).

8. 8
Who we are
Paco Sanchez is the most recent partner at Indizen
Technologies. He has joined the company to develop and
expand the consulting branch Indizen Quantitative
Solutions with a particular focus in providing quantitative
consulting services to Large Corporations and Financial
Institutions.
Until June 2009 Paco pursued a successful fourteen-
year career at Santander, where he became Global Head
of Risk Methodologies after having attained other
managerial and quantitative roles. As the global head of risk methodology, he
was responsible for all of the risk modeling factory, from steering the design of
quantitative tools used for credit and market risk management to leading the
definition of the group wide economic capital model. He supervised the
development of the rating and scoring models, the development of pricing
models used for model validation and all the quantitative support required from
the different Risk Management Areas.
He holds a Ph.D. in Physics from the Universidad Complutense de Madrid.

9. 9
Indizen Quantitative Solutions
indizen Quantitative models and tools
quantitative
solutions for the financial industry
IQS is a group of highly qualified specialists in the development of
IQS is a group of highly qualified specialists in the development of
quantitative models for the management and control of financial
quantitative models for the management and control of financial
risks.
risks.
We develop bespoke models and applications for risk
We develop bespoke models and applications for risk
management, valuation, pricing, rating, operations control and
management, valuation, pricing, rating, operations control and
end-of-day reconciliation.
end-of-day reconciliation.
We have a set of software libraries for quantitative analysis and risk
We have a set of software libraries for quantitative analysis and risk
management that can be implemented into our clients’ systems,
management that can be implemented into our clients’ systems,
giving them the ability increase their quantitative power in a cost
giving them the ability increase their quantitative power in a cost
effective way.
effective way.

10. 10
Services
We help organizations to improve their risk assessment and evaluation. We are specialist
in risk management and portfolio analysis.
Banking
Banking
Financial
Financial Treasury
Treasury book
book
Institutions
Institutions Risk
Risk
Function
Function
Institutional
Institutional
Investor
Investor Infrastructure
Infrastructure
Governance
Governance Control
Control & Methodology
& Methodology
Organization
Organization Risk appetite Models
Risk appetite Models
Policies Planning Platforms
Policies Planning Platforms
Strategy Metrics && Limits
Large Strategy Metrics Limits Research
Research
Large Compliance
Compliance Risk assessment
Risk assessment
Corporations
Corporations Action plans
Action plans
Areas of expertise

11. 11
Services
We provide quantitative consulting services, software libraries and systems to
help organizations better measure and anticipate risks and make the best business
decisions.
Valuation Reporting
Quantitative Resources
Quantitative Resources
Pricing
Pricing and / / or
and or Metrics
Metrics
models
models
Financial Library
Financial Library
Market and Simulation Scenario analysis
Simulation
Credit Risk models
models Economic Capital

12. 12
Services
Our models provide a quick solution for market and credit risk and give an answer to
problems of increasing importance such as Incremental Risk Charge and a proper
computation of Potential Future Exposure, features that are fully integrated in our
engines.
Our professionals have also extensive experience in modeling of structural risks,
scenario analysis, stress testing, credit scoring and rating models.
Our modular methodology can combine market, credit and
!
! operational risk into a unique risk model.
We place special care in developing a model that can be integrated
!
! into different pre-existing platforms with the advantage of it being
based in an open and low cost technological infrastructure.

13. 13
Services
Large Corporations and Institutional Investors usually have large portfolios exposed to
financial risks.
Portfolio Analysis We help organizations anticipate the risks that threaten their portfolios and
We help organizations anticipate the risks that threaten their portfolios and
Portfolio Analysis identify ways of preventing them from arising.
identify ways of preventing them from arising.
Corporations that do not have large teams of quantitative resources can
Corporations that do not have large teams of quantitative resources can
take advantage of our services to elaborate aafull portfolio’s risk profile.
take advantage of our services to elaborate full portfolio’s risk profile.
Portfolio Hedging
Portfolio Hedging As aaconsequence of the simulations performed, optimal hedging
As consequence of the simulations performed, optimal hedging
strategies are proposed so that the risk profile of your portfolio matches
strategies are proposed so that the risk profile of your portfolio matches
your risk appetite without spending aalot of money in quantitative analysts.
your risk appetite without spending lot of money in quantitative analysts.
Fair Pricing
Fair Pricing We provide aafull analysis of each new deal. Our simulations allow us to
We provide full analysis of each new deal. Our simulations allow us to
properly compute potential future exposure which will be used by financial
properly compute potential future exposure which will be used by financial
institutions to charge you for credit risk. A good understanding of the risk
institutions to charge you for credit risk. A good understanding of the risk
profile of each new deal can help your organization better negotiate aafair
profile of each new deal can help your organization better negotiate fair
price for your deals, saving money for your organization.
price for your deals, saving money for your organization.

14. 14
Services
Our risk model is a modular, scalable solution that can be easily adapted to the needs of
our clients no matter how sophisticated their requirements are.
Simulation Mapping Valuation Aggregation
Risk
Risk Risky
Risky Simulated
Simulated Risk
Risk
Drivers
Drivers Objects
Objects Values
Values Distributions
Distributions
Sources of risk: Curves, FX rates, Market value
Market Sources of risk:
Market prices,
Curves, FX rates,
Vol surfaces
Market value
changes
Risk Market prices, Vol surfaces changes
Principal compo-
Principal compo-
nents…
nents…
Synthetic Indices Credit Worthiness: Credit losses due
Credit Synthetic Indices Credit Worthiness: Credit losses due
Macro variables Rating / Scoring to default and
Risk Macro variables Rating / Scoring to default and
rating migration
rating migration
Other … … … …
Risks

15. 15
Services
For those firms that already have their own risk engine we also provide an aggregation
methodology that allows the estimation of Economic Capital.
ECONOMIC
CAPITAL
25
Business and
Market Risk 20
strategic risks
20 35
15
18
30
16
10
14 25
12
20
5
10
8 15
0
6
10
4
5
2
0 0
Credit Risk Reputational Risk
25 60
50
20
40
15
30
10 Operational Risk 20
35
5
10
30
0 0
25
20
15
10
5
0

16. 16
Recent Experiences
Market Risk Model We developed the market risk engine for aalarge international bank and aa
We developed the market risk engine for large international bank and
Market Risk Model number of institutional investors are currently using our models.
number of institutional investors are currently using our models.
Credit Risk Model We are participating in aa project for aalarge institution improving its credit
We are participating in project for large institution improving its credit
Credit Risk Model risk assessment by better estimating credit exposure.
risk assessment by better estimating credit exposure.
Economic Capital We have helped aamajor bank to develop an aggregation engine used to
We have helped major bank to develop an aggregation engine used to
Economic Capital aggregate risks into aaunique Economic Capital figure.
aggregate risks into unique Economic Capital figure.
Portfolio Analysis We have developed aaPortfolio Analysis Software Suite (PASS) in order to
We have developed Portfolio Analysis Software Suite (PASS) in order to
Portfolio Analysis help institutions better understand their portfolios and find the best hedging
help institutions better understand their portfolios and find the best hedging
strategies.
strategies.
Rating Models We offer an innovative rating methodology that is of special interest when
We offer an innovative rating methodology that is of special interest when
Rating Models applied to low default portfolios.
applied to low default portfolios.
Pricing Models We are currently providing several banks and institutions with pricing
We are currently providing several banks and institutions with pricing
Pricing Models models for treasury instruments. We are also helping them integrate the
models for treasury instruments. We are also helping them integrate the
pricing libraries into their own systems.
pricing libraries into their own systems.

17. 17
Recent Experiences
Worked examples

18. 18
Market Risk Model
Our methodology is based on the full revaluation of the portfolios in multiple
scenarios simulated either Historically or by Monte Carlo methods.
We apply stochastic evolution
models for market factors in
order to generate future 25
Simulation
scenarios. Portfolios are then 20
priced under each scenario to 15
10
get future value distributions. 5
0
The advantage of this
methodology is that it can be
applied both for market and
credit risk, producing both VaR Valuation Aggregation
and credit exposure as well as it
facilitates risks aggregation.

19. 19
Market Risk Model
Simulation Mapping Valuation Aggregation
Market
Market Market
Market Simulated
Simulated Risk
Risk
Drivers
Drivers Factors
Factors Values
Values Distributions
Distributions
Identify sources Apply a Simulate Correlated
of risk Evolution Model Changes
• Individual Risk Factors • Time series
• Principal Components
• Stocks • Volatilities
• Indexes
• FX rates • Correlations
• …
scenario
• Evolution models
•(Mean Reverting) Normal MDC
•(Mean Reverting) LogNormal time
step market driver

20. 20
Market Risk Model
Simulation Mapping Valuation Aggregation
Market
Market Market
Market Simulated
Simulated Risk
Risk
Drivers
Drivers Factors
Factors Values
Values Distributions
Distributions

21. 21
Market Risk Model
Simulation Mapping Valuation Aggregation
Market
Market Market
Market Simulated
Simulated Risk
Risk
Drivers
Drivers Factors
Factors Values
Values Distributions
Distributions

22. 22
Market Risk Model
Simulation Mapping Valuation Aggregation
Market
Market Market
Market Simulated
Simulated Risk
Risk
Drivers
Drivers Factors
Factors Values
Values Distributions
Distributions
Market Factors are defined as any risky parameters that are required as an input of a
pricing function (pricer) to compute the market price of a financial instrument.
The mapping process applies all simulated changes to the market factors Base
Scenario in order to generate a cube of scenarios of potential values for each of the
risk factors within each time step of the simulation.
scenario
Mapping
scenario
MDC
time
step market driver
MFC
time
Proxy Base step market factor
Scenario
market market market Simulated
driver factor factor values

23. 23
Market Risk Model
Simulation Mapping Valuation Aggregation
Market
Market Market
Market Simulated
Simulated Risk
Risk
Drivers
Drivers Factors
Factors Values
Values Distributions
Distributions
The valuation process generates a cube of potential future values for each security in the
portfolio at each scenario and time step.
scenario
scenario
MFC Valuation IVC
time
step market factor
time
step instrument value
Instruments Pricers
definitions

24. 24
Market Risk Model
Simulation Mapping Valuation Aggregation
Market
Market Market
Market Simulated
Simulated Risk
Risk
Drivers
Drivers Factors
Factors Values
Values Distributions
Distributions

25. 25
Market Risk Model
Simulation Mapping Valuation Aggregation
Market
Market Market
Market Simulated
Simulated Risk
Risk
Drivers
Drivers Factors
Factors Values
Values Distributions
Distributions
scenario
scenario
Aggregation
IVC
time time
step instrument value step
portfolios portfolio value

26. 26
Market Risk Model
Simulation Mapping Valuation Aggregation
Market
Market Market
Market Simulated
Simulated Risk
Risk
Drivers
Drivers Factors
Factors Values
Values Distributions
Distributions
scenario
scenario
scenario
IVC
scenario
MFC
MDC time
time time time
step market driver step market factor step instrument value step
portfolio value

27. 27
Credit Risk Model
Based on the same foundations we simulate the evolution of the credit quality
of the counterparties and estimate the value of the portfolios in each
scenario.
We can provide an independent
Credit Risk Engine or, Simulation
25
alternatively, an integrated 20
15
Market-Credit engine. 10
5
In case an independent engine is 0
chosen, a later aggregation is
possible by means of our
aggregation methodology.
Valuation Aggregation

28. 28
Credit Risk Model
Simulation Mapping Valuation Aggregation
Credit
Credit Simulated
Simulated Risk
Risk
CWI
CWI
Drivers
Drivers Losses
Losses Distributions
Distributions
Hypothesis:
The credit worthiness is an unobservable variable that can be modeled by means of a
linear combination of observable variables such as economic indicators, i.e. GDP, rates,
indexes… plus a specific factor depending only on each counterparty.
Yi
Systemic risk Specific Risk
Global factor Country factor Industry factor

29. 29
Credit Risk Model
Simulation Mapping Valuation Aggregation
Credit
Credit Simulated
Simulated Risk
Risk
CWI
CWI
Drivers
Drivers Losses
Losses Distributions
Distributions
es
Global Economy Japan
ex
US China
c Ind of
eti d out es
Brazil India
Mexico Other Asia
th
Wholesale Other LatAm Finance yn nde pric
S le
UK
Germany
Industrial
Oil & Gas b exes
France
Other Europe
Electricity
Telecom
ind
Middle East Services
Per country / market:
•Projection of the Global Economy
Local Factor
over the local market
GDP
Retail Interest Rates
Unemployment •Observed values
House Prices

30. 30
Credit Risk Model
Simulation Mapping Valuation Aggregation
Credit
Credit Simulated
Simulated Risk
Risk
CWI
CWI
Drivers
Drivers Losses
Losses Distributions
Distributions
Wholesale
K
Yi = ∑ wij Z j + 1− Ri2 ε i
Global Top 10 Bank
j =1
Zj Orthogonal Credit Drivers
K
R = ∑ wij
2 2
i
j =1
Services
Japan
India
Industrial
Telecom
Mexico
France
Other Europe
China
Other Asia
Finance
Brasil
Other Latam
US
UK
Middle East
Global Economy
Germany
Oil & Gas
Electricity

31. 31
Credit Risk Model
Simulation Mapping Valuation Aggregation
Credit
Credit Simulated
Simulated Risk
Risk
CWI
CWI
Drivers
Drivers Losses
Losses Distributions
Distributions
Wholesale
The credit worthiness of the counterparties is
mapped into rating by means of the observed Rating
Transition Matrix.
 
Yi = w1,i ·Z1 + w2 ,i ·Z 2 + L + wN ,i ·Z N + 1 − ∑ w2,i ·ε i
 j 
 j 
CCC AA
AAA AA A BBB BB B CCC D DEF B BB BBB A AAA
AAA 71.55% 19.86% 5.43% 1.90% 0.24% 0.37% 0.58% 0.07%
AA 2.18% 71.06% 21.14% 4.14% 0.70% 0.29% 0.29% 0.20%
A 0.18% 6.43% 69.72% 19.47% 2.54% 0.80% 0.51% 0.35%
BBB 0.06% 1.10% 16.43% 64.74% 11.26% 3.84% 1.77% 0.80%
BB 0.07% 0.64% 5.39% 27.86% 43.23% 14.34% 6.87% 1.60%
B 0.02% 0.42% 3.12% 12.95% 16.48% 45.46% 18.55% 3.00%
CCC 0.16% 0.61% 2.36% 3.75% 4.26% 8.67% 74.19% 6.00%
D 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00%
-4 -3 -2 -1 0 1 2 3 4

32. 32
Credit Risk Model
Simulation Mapping Valuation Aggregation
Credit
Credit Simulated
Simulated Risk
Risk
CWI
CWI
Drivers
Drivers Losses
Losses Distributions
Distributions
Wholesale
For each rating migration an economic equivalent amount is computed.
If a default occurs
the loss is equal to Li = 1 − Recovery
the amount that
cannot be recovered
If a migration occurs  t rrf + si 1 
Li = 1 − ∑ +
the loss is equal to
the difference in  i =1
 (1 + rrf + s f )i (1 + rrf + s f )t  

spreads  (rrf + si )(1 + rrf + s f )t + (rrf + s f ) − (rrf + si )
= 1−  

 (rrf + s f )(1 + rrf + s f )t 


33. 33
Credit Risk Model
Simulation Mapping Valuation Aggregation
Credit
Credit Simulated
Simulated Risk
Risk
CWI
CWI
Drivers
Drivers Losses
Losses Distributions
Distributions
Retail
The state of the economy is simulated by means of the different credit drivers plus a Local
Latent Factor.
GDP, PPP
Delinquency Rate 7,00
14,00 6,00
5,00
 N 
Yi = β i  wL Z L + ∑+1 
wij Z j  + 1− Ri2 ε i
12,00 4,00
3,00
10,00 2,00

 
1,00
8,00 0,00
j=K
-1,00
6,00 -2,00
1980 1985 1990 1995 2000 2005 2010
4,00
N
R =w + ∑w
2,00
Unemployment 2 2 2
30,00
0,00 i L ij
j = K +1
25,00
1987 1990 1993 1995 1998 2001 2004 2006
20,00
15,00
10,00
 2 N 
 wL + ∑ wij ∑ jk wki 
5,00
18,00
Inflation 0,00
1980 1985 1990 1995 2000 2005 2010 βi = R i
2
 
 
16,00
14,00 j ,k = K +1
12,00
10,00
8,00
6,00
4,00
2,00
0,00
1980 1985 1990 1995 2000 2005 2010

34. 34
Credit Risk Model
Simulation Mapping Valuation Aggregation
Credit
Credit Simulated
Simulated Risk
Risk
CWI
CWI
Drivers
Drivers Losses
Losses Distributions
Distributions
Retail
The state of the economy is simulated by means of the different credit drivers plus a Local
Latent Factor.
 N 
Yi = β i  wL Z L +
 ∑+1wij Z j  + 1− Ri2 ε i

Global  j=K 
Economy
The Local Latent Factor is the projection of
the Global Economy Factor over each
Country/Region
Z iL = α i Z1 + 1− α i2 ε L
Z iL = (sin δ i ) Z1 + (cos δ i )ε L

35. 35
Credit Risk Model
Simulation Mapping Valuation Aggregation
Credit
Credit Simulated
Simulated Risk
Risk
CWI
CWI
Drivers
Drivers Losses
Losses Distributions
Distributions
Retail
Each state of the economy has an expected/plausible level of losses.
For a typical granular,
 N −1 ( pd ) − ρ Y 
homogeneous retail Li = N  i i i

portfolio, such level of 
 1 − ρi2


losses is given by:

36. 36
Credit Risk Model
Simulation Mapping Valuation Aggregation
Credit
Credit Simulated
Simulated Risk
Risk
CWI
CWI
Drivers
Drivers Losses
Losses Distributions
Distributions
A common set of credit drivers gives
30
us the ability to aggregate both worlds:
25
Retail Wholesale Retail
20
15
10
25
5
20
0
15
10
5
25
Wholesale
0
20
15
10
5
0
Global
Economy Local Simulated Credit
Latent Factors Losses Distribution
Wholesale Retail
Credit Drivers Credit Drivers

37. 37
Credit Risk Model
A Three Layers Model
View
View Portfolio
Portfolio Counterparty
Counterparty Deal
Deal
s
tie
Monte Carlo MonteliCarlo
bi
Methodo-
Methodo-
Monte Carlo sta
Monte Carlo
in Or
Closed Form
Closed Form
or
logy or Or Equation
logy Analytical (CGF) Analytical (CGF) Equation
Analytical (CGF) Analytical (CGF)
Intraday, on-line
Intraday, on-line
Complete calculation
Complete calculation Allocation at calculations for new or
Allocation at calculations for new or
that can incorporate counterparty level. existing deals.
Uses
Uses that can incorporate
all the necessary
counterparty level. existing deals.
all the necessary
hypothesis for aa Very fast and stable Its stability makes it
hypothesis for Very fast and stable Its stability makes it
complete calculation. calculation. appropriate for
complete calculation. calculation. appropriate for
RAROC calculations.
RAROC calculations.

38. 38
Economic Capital
Institutions, in general, use different risk engines to compute the
different risks. Our methodology allows the aggregation of all risks,
regardless of its nature, confidence level and time horizon, into a
unique losses distribution.
ECONOMIC
CAPITAL
25
Business and
Market Risk 20
strategic risks
20 35
15
18
30
16
10
14 25
12
20
5
10
8 15
0
6
10
4
5
2
0 0
Credit Risk Reputational Risk
25 60
50
20
40
15
30
10 Operational Risk 20
35
5
10
30
0 0
25
20
15
10
5
0

39. 39
Economic Capital
How to combine different risk types and models into a unique model?
Marginal
Marginal Correlation
Correlation Copula
Copula
Distributions
Distributions
11 Characterization of
Characterization of
33 Find aa set of Risk
Find set of Risk
55 Obtain the loss for each
Obtain the loss for each
risk distributions by Drivers and estimate the type of risk: estimate
type of risk: estimate
risk distributions by Drivers and estimate the
computing the first four combination that govern the loss via the inverse
computing the first four combination that govern the loss via the inverse
moments each type of risk cumulative distribution
cumulative distribution
moments each type of risk
2 Extend distributions 4 Simulate scenarios for 6 Sort losses properly
Sort losses properly
2 Extend distributions 4 Simulate scenarios for 6
to aa common Time in order they present the
to common Time the Risk Drivers and
the Risk Drivers and in order they present the
Horizon by applying the generate aa loss percentile correlations shown in
Horizon by applying the generate loss percentile correlations shown in
“constant level of risk” for each marginal loss their respective risk
“constant level of risk” for each marginal loss their respective risk
concept distribution engines
engines
concept distribution

40. 40
Economic Capital
Risk Adjusted Return
-Expected loss
+Capital Return
+/- Transfer prices
- Expenses
-Taxes
RAROC
RAROC ==
Capital
Required as a protection
against unexpected losses
(minus expected losses) for the
defined confidence level

41. 41
Economic Capital
Two visions
• Measures the expected profitability on capital for the
RAROC Op next 12 months
Pre-deal • Based on estimations of expected income
Profitability of
the deal.
(ExpectedGrossIncome(1 − CostToIncome) − ExpectedLoss )(1 − TaxRate)
Capital
• It is the profitability on capital according to the
RAROC Cl income and capital realized during the last 12 months
Post-deal • Based on recorded income and averaged capital over
Profitability of last last year.
the client.
(RealizedGrossIncome(1 − CostToIncome) − ExpectedLoss )(1 − TaxRate)
Capital

42. 42
Economic Capital
• The use of these two measures allow a quick evaluation of how
a new deal affects the portfolio
Capital Cl * RAROC Cl + Capital Op * RAROC Op
RAROC Cl(+n) ≈
Capital Cl + Capital Op
• Both visions have a limited horizon of one year.
• It is possible to extend our vision to a lifetime measure that
estimates an average profitability during the life of the deal.

43. 43
Economic Capital
Lifetime RAROC
Time Expected Economic Capital Interest on Net
Exposure Provisions Return
(years) Loss Capital Flow Capital Cash Flow
0 100.000.000 315.209 6.040.455 -6.040.455 -315.209 -6.355.664
1 100.000.000 434.070 7.089.544 -1.049.088 302.023 -434.070 1.500.000 318.865
2 100.000.000 531.092 7.796.903 -707.359 354.477 -531.092 1.500.000 616.026
3 100.000.000 610.600 8.287.775 -490.872 389.845 -610.600 1.500.000 788.372
4 100.000.000 674.832 8.621.210 -333.435 414.389 -674.832 1.500.000 906.122
5 100.000.000 725.335 8.831.802 -210.592 431.061 -725.335 1.500.000 995.134
6 100.000.000 763.432 8.942.983 -111.181 441.590 -763.432 1.500.000 1.066.977
7 100.000.000 790.377 8.972.222 -29.239 447.149 -790.377 1.500.000 1.127.533
8 100.000.000 807.395 8.933.351 38.871 448.611 -807.395 1.500.000 1.180.088
9 100.000.000 815.671 8.837.737 95.614 446.668 -815.671 1.500.000 1.226.611
10 100.000.000 0 0 8.837.737 441.887 0 1.500.000 10.779.624
IRR 15,5%

44. 44
Portfolio Analysis
Our risk engines give us the ability to simulate the behavior of our
customer’s portfolios in order to identify the principal risk factors and
allow us to check the performance of different hedging strategies.
Before
Before After
After
35.000.000 35.000.000
30.000.000 30.000.000
25.000.000 25.000.000
20.000.000 20.000.000
15.000.000 15.000.000
10.000.000 10.000.000
5.000.000 5.000.000
0 0
1-ago-09
1-ago-10
1-ago-11
1-ago-12
1-ago-13
1-ago-14
1-ago-15
1-ago-16
1-ago-17
1-ago-18
1-ago-19
1-ago-20
1-ago-09
1-ago-10
1-ago-11
1-ago-12
1-ago-13
1-ago-14
1-ago-15
1-ago-16
1-ago-17
1-ago-18
1-ago-19
1-ago-20
Notional Instrument Rate Maturity Notional Instrument Rate Maturity
200.000.000 Payer 3,00% Jun 2019 200.000.000 Payer 3,00% Jun 2019
125.000.000 Receiver 3,84% Mar 2015 125.000.000 Receiver 3,84% Mar 2015
150.000.000 Receiver 3,30% Jun 2018 150.000.000 Receiver 3,30% Jun 2018

45. 45
Portfolio Analysis
Generate scenarios for the risk factors that we want to stress
4.90
4.80
We apply statistical models to give a
4.70 dynamics to the risk factors:
4.60
4.50 •Interest rates
Interest rate
4.40
•FX rates
4.30
4.20
•Share prices
4.10 •Volatilities
4.00 •Correlations
3.90 •Solvency
3.80
0 1 2 3 4 5 6
•
Time (years) •
•

46. 46
Portfolio Analysis
Valuate the portfolio under each scenario
20
By pricing the portfolio under each 15
scenario in different future times we 10
Value (EUR x1000)
can determine which is the worst 5
situation, which are the risk factors 0
that cause such situation and when it -5
can happen. -10
-15
As a result hedging strategies can be
-20
proposed. 0 1 2 3 4 5 6
Time (years)

47. 47
Portfolio Analysis
Scenario generation Pricing
4.90 20
4.80 15
Valor del Swap (EUR x1000)
4.70
10
4.60
Tasa de interés
4.50 5
4.40
0
4.30
4.20 -5
4.10 -10
4.00
-15
3.90
3.80 -20
0 1 2 3 4 5 6 0 1 2 3 4 5 6
Tiempo (años) Tiempo (años)
Identification of the adverse cases
AND
AND Design a hedging strategy …
THEN
THEN … and run the portfolio again

48. 48
Portfolio Analysis
Our methodology allows to properly capture some effects
otherwise unobserved
Portfolio effect or how the adverse effects of some deals can be netted
by other deals.
Deal A Deal B
The portfolio can behave
better than any of its deals
rates rates
Correlation or how new deals with a counterparty can help lower its risk
exposure.
Optimum Pricing, when a deal mitigates the risk exposure with a
customer, a better price than the market can be offered.

49. 49
Portfolio Analysis
We aim to answer the following questions:
Which is the maximum risk scenario? And, how feasible is it?
What risk mitigants can help the deal to lower its risk profile?
How does a particular deal affect the rest of the portfolio?
What is the profitability of a portfolio compared to its level of risk?
Is there any relationship between the risk profile of the deal and the
credit quality of the counterparty (wrong way exposure)?
How can some legal agreements help obtain a better deal (ISDA,
CSA, …)?

50. 50
Rating Models
In the case of low default portfolios expert
judgment models are a common practice in the
market place; however, the use of more objective,
quantitative techniques is a requisite that allows
for a transparent and efficient business model.
We develop quantitative rating models for low
default portfolios and SME.

51. 51
Rating Models
A rating model is an ordering criterion
to facilitate credit decisions goods
Decision point
Goods
Bads
scoring/rating
Type II error Type I error
Cost of opportunity Credit Risk
bads
The success of a rating model depends on its ability to separate the good
customers from the bad ones, thus showing a correlation between the
defined ordering criterion and the occurrence of credit events.

52. 52
Rating Models
A rating model is built by maximizing the powerstat of an ordering criteria
10
The best possible model
10
Defaults
Defaults
5
5
Total population
Total population The worst of the models
10
Powerstat = B/A
Defaults
A
B 5
Total population

53. 53
Rating Models
What to do when there are not enough defaults?
We use the CDS market to establish an objective ordering criteria.
CDS spreads are averaged over a defined time window.
This ordering criteria is mapped to real world distances to default.
A statistical model is developed that explains the distances to default
(or pd) by means of financial statements and balance sheets ratios.
This model is extended to all counterparties, including those with a CDS
and those without it.
CDS spreads Average CDS spreads over time
25
Merton-like model to map to DtD
20
Anchoring to PD (real world)
15
bp
Statistical model via regression
10
to financial statements
5
Map PD from statistical model to
0
Time
rating

54. 54
Rating Models
Example of implementation of a LDP rating
Counterparties with a CDS
CDS Spreads
Financial
Financial
Statements
Statements
Risk neutral DtD dtd ∗
Statistical
Real world DtD dtd = dtd ∗ + µ Statistical
Model
Model
Probability of default (
pd = N −1 dtd ∗ + µ ) PD
PD
All Counterparties
All Counterparties
Master Scale
Best agreement to aa
Best agreement to
reference, i.e. CAPM,
reference, i.e. CAPM, RATING
Merton, rating agency, …
Merton, rating agency, … RATING

55. 55
Pricing Models
Pricing models are complex mathematical functions that make many assumptions:
There is not such a thing as a complete Pricing
Van1y: Spot price paths; HedgeFreq: 0.25 days
Model. 1.8
 dS = µdt + vdW
 t
1.7
S
Pricing models are only approximations to the real dv = κ (θ − v) dt + σdYy
1.6 
price of financial products. < dWt , dYt > = ρdt
1.5
Spot price
1.4
A model does necessarily impose some 1.3
simplifications in the fundamental hypothesis. 1.2
In banking there is not a lab where models can be 1.1
tested. 1
0.9
Mar06 May06 Jun06 Aug06 Sep06 Nov06 Jan07 Feb07 Apr07
The uncertainty of the market adds some complexity
to the problem.
S5
p2 A great deal of expertise is required to construct
S2
p0
1-p2
such pricing functions. We have proven expertise
S0 S4
1-p0
p1 in the development of pricing models for all types
S1
1-p1
S3
of exotic derivatives.
t= δ
t=δt δ
t=2·δt

56. 56
Pricing Models
Black-
Closed form Scholes
Trees
Calibration
Numerical Monte Carlo required
PDE

57. 57
Pricing Models
Models based on the Black-Scholes equation
dS = S µ ·dt + S ·σ ·dW t
Randomness factor
Changes in
the stock price
Drift rate Time increment Scale for the
Randomness factor
Pros Cons
Closed form solutions Constant parameters (rates, vols,
dividends)
Only applicable to vanilla
instruments.

58. 58
Pricing Models
Trees
S5 C5
p2 p2
S2 C2
p0 p0
1-p2 1-p2
S0 S4 C0 C4
p1 p1
1-p0 1-p0
S1 C1
1-p1 S3 1-p1 C3
t=0 δ
t=δt δ
t=2·δt t=0 δ
t=δt δ
t=2·δt
Pros Cons
Fast computing Numerical errors
Account for temporal structure of rates, Not applicable to multiple underlying
vols and dividends products
Appropriate for American and Barrier
options

59. 59
Pricing Models
Examples: Binomial tress
Jarrow-Rudd (JR) Cox-Ross-Rubinstein (CRR) Trigeorgis (TRG)
Sup = Snow·u Sup = Snow·u Sup = Snow·u
Sdown = Snow·d Sdown = Snow·d Sdown = Snow·d
1
 1 2
 r −q − σ  ∆T +σ ∆T ν = r −q− σ2
u=e  2 
u = eσ ∆T 2
σ 2∆T +ν 2 ∆T 2
−σ ∆T u=e
 1 2
 r −q − σ  ∆T −σ ∆T d =e
d =e  2 
d = e− σ ∆T +ν ∆T
2 2 2
( r −q ) ∆T −σ ∆T
e −e
1 p= ν∆T
p= eσ ∆T
− e−σ ∆T 1 1
p= + ·
2 2 2 σ 2∆T +ν 2 ∆T 2
Example: Hull-White model
drt = (θt − at ·rt )·dt + σ t ·dWt