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Market Risk Stress Testing ModelsDr. JUAN M. LICARI, SENIOR DIRECTOR

HEAD OF ECONOMIC & CONSUMER CREDIT ANALYTICS – EMEA

Sponsored by:

2

Modelling Interest Rates and Market FactorsLeading Examples

(1) Swaps and Sovereign Curves (term structure models for interest rates)Principle component approach

(2) Stock Market Returns, Historical and Implied VolatilitiesTime series model with conditional heteroskedasticity and Global Equity Factor (GEF) related to global economic conditions

(3) Mortgage-backed Securities: Agency and Non-agencyTerm structure models with GEF and prepayment factor

(4) Corporate CDS and Corporate Bond Spreads by Sector and Rating CategoryTime series model with Global Credit Factors, combined with principal component analysis

(5) Sovereign CDS by Country and MaturityTime series model with long memory, combined with principal component analysis

(6) Credit MigrationTransition matrices for credit portfolios, two-stage approach: (i) discrete-choice model combined with (ii) quantile and time-series analysis

3

Overall Modelling Approach1

4

Map alternative scenarios assumptions to market risk variables in multivariate, parametric and

semi-structural framework.

Satellite models allow for explicit and transparent connection to core drivers; no feedback between

satellite variables z and core drivers (x,y).

Model selection is based on a combination of economic theory, regulatory assumptions, and the

statistical properties of estimated model.

Models have reasonable in-sample fit; produce consistent, sensible forecasts and stressed

scenarios out of sample.

Market Risk Stress Testing Models

CORE MODEL

Satellite Model 1

Satellite Model 3

Satellite Model S Satellite Model 2

5

Potential core drivers identified based on macroeconomic intuition and consistency with regulatory

assumptions.

The potential drivers undergo the exhaustive search process to obtain the most robust and

predictive model available from the tested variables.

Typical exhaustive search criteria include:

• All possible combinations of potential drivers (including lags)

• A max number of macro drivers selected

• No strong correlation between drivers

• Coefficient estimates must be statistically significant

• Expected signs and magnitude of the estimates

• Maximization of a target index (e.g. Adjusted R² /RMSE, Log-likelihood, AIC, MAE, etc.)

Model Selection Procedure

6

Post-estimation analysis

Diagnostic methods to verify regression model assumptions and detect. Residual & outlier analysis, in-

sample goodness of fit.

Beta elasticities

Quantifies the response of the dependent variable to a 1 standard-deviation shock on each driver.

Impulse-response analysis

Time-series analysis of the effect of a permanent and/or temporary shock (e.g. 1 standard-deviation)

applied to any given driver. The output is the response function (over time) of our endogenous variable

to an impulse on any of the drivers.

Backtesting

Remove parts of the sample data from the model estimation and use the model to generate forecasts

for the resulting holdout sample to assess model accuracy.

Typical Model Validation

7

-.1

-.05

0.0

5

-6-4

-20

2

GG

F

2000q1 2005q1 2010q1 2015q1 2020q1

GGF US GDP YoY Growth

UK GDP YoY Growth EUR GDP YoY Growth

JPN GDP YoY Growth

PRA Baseline

Global GDP GrowthModel DriversGlobal Growth Factor (GGF)

-6-4

-20

2

2000q1 2005q1 2010q1 2015q1 2020q1Time

PRA BL PRA ST

Alternative Scenarios

Global Growth Factor

-.1

-.05

0.0

5

-6-4

-20

2

GG

F

2000q1 2005q1 2010q1 2015q1 2020q1Time

GGF US GDP YoY Growth

UK GDP YoY Growth EUR GDP YoY Growth

JPN GDP YoY Growth

PRA Stress

Global GDP Growth

8

-.4

-.2

0.2

.4.6

-4-2

02

4

GE

F

2000q1 2005q1 2010q1 2015q1 2020q1

GEF EUR Equity YoY Growth

US Equity YoY Growth UK Equity YoY Growth

JPN Equity YoY Growth

PRA Baseline

Global Equity Growth

-4-2

02

4

2000q1 2005q1 2010q1 2015q1 2020q1Time

PRA BL PRA ST


Global Equity Factor

-.4

-.2

0.2

.4.6

-4-2

02

4

GE

F

2000q1 2005q1 2010q1 2015q1 2020q1Time

GEF EUR Equity YoY Growth

US Equity YoY Growth UK Equity YoY Growth

JPN Equity YoY Growth

PRA Stress

Global Equity Growth

Model Drivers (cont.)Global Equity Factor (GEF)

9

10

20

30

40

50

60

-20

24

6

GE

VF

2000q1 2005q1 2010q1 2015q1 2020q1

GEVF VIX INDEX

VSTOXX VNKY

VFTSE US Volatility, PRA BL

PRA Baseline

Global Equity Volatility

-20

24

6

2000q1 2005q1 2010q1 2015q1 2020q1Time

PRA BL PRA ST


Global Equity Volatility Factor

10

20

30

40

50

60

-20

24

6

GE

VF

2000q1 2005q1 2010q1 2015q1 2020q1Time

GEVF VIX INDEX

VSTOXX VNKY

VFTSE US Volatility, PRA ST

PRA Stress


10

20

30

40

50

60

-20

24

6

GE

VF

2000q1 2005q1 2010q1 2015q1 2020q1

GEVF VIX INDEX

VSTOXX VNKY

VFTSE US Volatility, PRA BL

PRA Baseline


10

20

30

40

50

60

-20

24

6

GE

VF

2000q1 2005q1 2010q1 2015q1 2020q1Time

GEVF VIX INDEX

VSTOXX VNKY

VFTSE US Volatility, PRA ST

PRA Stress


Model Drivers (cont.)Global Equity Volatility Factor (GEVF)

10

0

.05

.1.1

5.2

.25

Den

sity

-5 0 5 10 15 20Max Drop in Cumulative GDP Growth, %

Density Function

-6-4

-20

24

GD

P G

row

th,

% Q

/Q

+Q1 +Q2 +Q3 +Q4 +Q5 +Q6 +Q7 +Q8 +Q9

GDP Growth, % Q/Q: Forecasts per Quarter

Max Cumulative Drop

in GDP growth

Scatter over Marginal

Rank Order

Cu

mu

lative

Pro

po

rtio

n

Max cumulative drop in GDP Growth

Example of a Marginal Loading into Overall Scenario

Rank-Ordering Algorithm

Macroeconomic Scenario Simulations

11

Macroeconomic Scenario Simulations (cont.)

46

81

01

21

41

6

Une

mplo

ym

en

t R

ate

, %

Block 1 Block 2 Block 3 Block 4 Block 5

Unemployment Rate, %: Over Scenario Blocks

-6-4

-20

24

GD

P G

row

th,

% Q

/Q


GDP Growth, % Q/Q: Over Scenario Blocks

12

Examples of Market Risk Models:Swap Rates, Bond Yields & Libor Rates

Equity Returns & VolatilitiesCorporate Credit Spreads

2

13

Swap RatesEuro curve level and slope factors with core drivers

-3-2

-10

12

Money M

ark

et R

ate

-10

-50

51

0

Level

2000m1 2005m1 2010m1 2015m1

Level Money Market Rate

Level Factor vs Money Market Rate

-10

12

DE

U 1

0y y

ield

-10

-50

51

0

Level

2000m1 2005m1 2010m1 2015m1

Level DEU 10y yield

Level Factor vs DEU 10y Yield

-10

12

3

Term

pre

miu

m

22

.53

3.5

4

Slo

pe

2000m1 2005m1 2010m1 2015m1

Slope Term premium

Slope Factor vs Term Premium

-.0

6-.

04

-.0

20

.02

.04

GD

P g

row

th, L2

22

.53

3.5

4

Slo

pe

2000m1 2005m1 2010m1 2015m1

Slope GDP growth, L2

Slope Factor vs GDP Growth

14

Swap Rates (cont.)Euro term structure history and forecasts, ECCA scenarios

02

46

Rate

s (

%)

2002m1 2006m1 2010m1 2014m1 2018m1

Baseline

02

46

Rate

s (

%)

2002m1 2006m1 2010m1 2014m1 2018m1

S3

02

46

Rate

s (

%)

2002m1 2006m1 2010m1 2014m1 2018m1

S4

02

46

Rate

s (

%)

2002m1 2006m1 2010m1 2014m1 2018m1

S8

15

Swap Rates (cont.)Euro term structure history and forecasts, CCAR scenarios

02

46

Rate

s (%

)

2002m1 2006m1 2010m1 2014m1 2018m1

Baseline

02

46

Rate

s (%

)

2002m1 2006m1 2010m1 2014m1 2018m1

Adverse

02

46

Rate

s (%

)

2002m1 2006m1 2010m1 2014m1 2018m1

Severely Adverse

16

Government Bond Yields

05

10

15

20

Yie

lds, %

3m 6m 1y 2y 3y 5y 7y 10y 20y 30y

Box-Plots Across Maturities at +Q9

Government Bond Yield Curves

17

Government Bond Yields (cont.)

05

10

15

Yie

lds, %


3 Months

05

10

15

20

Yie

lds, %


1 Year

05

10

15

20

Yie

lds, %


5 Years

05

10

15

20

Yie

lds, %


10 Years

Simulations over Scenario Blocks (1 for Good , 5 for Stressed) at +Q9

Government Bond Yields - Leading Maturities

18

Government Bond Yields (cont.)

0.2

.4.6

Density

0 2 4 6 8 10Term Premium (10y vs. 3m Spread, %)

Distribution for +Q9

0 2 4 6 8 10Yield Curve Slope (10y vs. 3m Spread, %)

Box-Plot for +Q9

02

46

810

Yie

ld C

urv

e S

lope

0 5000 10000 15000 20000 25000Simulation id (1 for Good , 25000 for Stressed)

+Q9 Values over Simulations

02

46

810

Yie

ld C

urv

e S

lope

+Q1 +Q2 +Q3 +Q4 +Q9 +Q6 +Q7 +Q8 +Q9

Box-Plots, all +Qs

Analysis Over Quarters and Simulations

Yield Curve Slope (10y vs. 3m Spread, %)

19

Equity Returns and VolatilitiesStock indexes history and forecasts, ECCA scenarios

4000

6000

8000

10000

2002m1 2006m1 2010m1 2014m1 2018m1

bl s3 s4 s8

UKX Index

1000

2000

3000

2002m1 2006m1 2010m1 2014m1 2018m1

bl s3 s4 s8

SPX Index

2000

3000

4000

5000

2002m1 2006m1 2010m1 2014m1 2018m1

bl s3 s4 s8

SX5E Index

20

Equity Returns and Volatilities (cont.)Implied 30-day volatility history and forecasts, ECCA scenarios

2040

60

2002m1 2006m1 2010m1 2014m1 2018m1

bl s3 s4 s8

V2X Index

1020

3040

50

2002m1 2006m1 2010m1 2014m1 2018m1

bl s3 s4 s8

VFTSE Index

020

4060

2002m1 2006m1 2010m1 2014m1 2018m1

bl s3 s4 s8

VIX Index

21

Equity Returns and Volatilities (cont.)Example of daily forecasts – Dow Jones Industrial Average

Forecast daily returns over time – consistent with Baseline & Severe Scenarios

-.03

-.02

-.01

0

.01

.02

41000 41500 42000 42500date_as_number

ff_dd_djia_s1 ff_dd_djia_bl

dd_djiaHistoric Values

Stressed Scenario Baseline Scenario

22

Corporate Credit SpreadsFinancials - over maturities and rating classes

0.5

11.5

2

Spre

ad, %

3m 1y 3y 5y 7y 10y 20y 30y

Aaa

05

10

15

Spre

ad, %

3m 1y 3y 5y 7y 10y 20y 30y

A

05

10

15

20

Spre

ad, %

3m 1y 3y 5y 7y 10y 20y 30y

Bbb

05

10

15

20

25

Spre

ad, %

3m 1y 3y 5y 7y 10y 20y 30y

B

5 Quarters out of Sample (+Q5) - Across Rating Classes

Corporate Spread Curves - Financials

23

Corporate Credit Spreads (cont.)5Y Credit Spreads for Financials - over quarters and ratings

0.5

11.5

2

Spre

ad, %

3m 1y 3y 5y 7y 10y 20y 30y

Aaa

05

10

15

Spre

ad, %

3m 1y 3y 5y 7y 10y 20y 30y

A

05

10

15

20

Spre

ad, %

3m 1y 3y 5y 7y 10y 20y 30y

Bbb

05

10

15

20

25

Spre

ad, %

3m 1y 3y 5y 7y 10y 20y 30y

B

5 Quarters out of Sample (+Q5) - Across Rating Classes

Corporate Spread Curves - Financials

24

Concluding Remarks

- Model set-up- Scenario-driven and simulated projections

- Leverage credit risk stress testing models to achieve consistent outcomes

3

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26

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market risk stress testing models - moody's analyticsmarket risk stress testing models ... modelling...

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