AIRC Seminar

Eric Yau Consultant, Barrie & Hibbert Asia Eric.Yau@barrhibb.com December 2012

Market Risk Modeling - An Introduction

Agenda

+ Introduction to market risk modeling – What we are trying to do here

– Common applications

– Components of ESG model

+ The devil is in the details (part 1)

– Constructing the initial yield curve

– Liquidity premium

– Mark-to-model in the absence of market prices

+ Workshop!

2 P.1

Introducing market risk modeling

3

What we are trying to do here

+ What is the fair valuation of embedded financial derivatives on my liability book? – Liability is not tradable

+ What are the risk exposures of my net assets, and how should I

measure them? – Risk exposure is multi-asset, multi-currency, multi-time period

+ What would my balance sheet look like in a probabilistic world? E.g.

what is the chance of having NAV less than X billion? – Developing a view above the future state (or distribution) of the world is a

subjective matter

+ How should I manage my asset-liability in light of such risks?

– Requires thorough understanding of the risk nature of assets and liabilities on your book

4 P.2

Model components

Economic scenarios: Base and Sensitivities

Liability Portfolio ALM System

Economic Assumption

Model Assumption

Model Choice

Market Data

calibration

Economic Scenario Generator

Asset Portfolio

Generate analysis for both asset and liability portfolios: * Valuation * Risk / Capital measures * Mismatch position

Risk Modeling Engine:

Projection Engine:

5

Economic Scenario Generator

ALM System

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

HKD

Mill

ions

What is ESG? – Monte Carlo Simulation

6

+ Produce economically coherent joint distributions of financial and economic factors.

+ Generated using sophisticated models that capture the dynamics of financial markets – dependency, tail risk etc.

Typical variables being modeled -

+ Interest rates

+ Inflation

+ Credit

+ Equity

+ Alternative investment

+ Option implied volatility

+ FX

Example output for interest rates

P.3

Common applications

7

Economic balance sheet

+ Mark-to-market (or mark-to-model) for both assets and liabilities

+ A better reflection of the true economics of the firm + MVL / MCEV calculation typically requires stochastic projection

– Liability = complex non-linear function of multiple risk factors

– Options and guarantees require stochastic quantification

8

Market value Market-

consistent value

Assets Liabilities

Economic Balance Sheet A

L

MCEV

Adjustment

P.4

Stochastic vs deterministic

+ We live in a probabilistic world + Example: interest rate

9

Actual interest rate (random)

Pricing / valuation interest rate (deterministic) Guaranteed rate

Expected Profit

How should we price in such an event?

Consideration + distributional assumption + parameters (e.g. volatility) + multi-asset + multi-time period + etc

Liability valuation / pricing + ESG model selection and calibration has to be appropriate for

liabilities – Model choice - simple vs complex

– Expert judgement must be prudent, reliable and justifiable

+ Using a richer model will make this easy to deliver in practice…

10 P.5

Equity volatility – simple models

11

Market Implied Volatility Surface ESG Generated IV Surface from a

simple model (TVDV)

+ Simple model only appropriate for limited range of liability valuations – eg all ATM

+ If not all, need to segment book… – Dependencies between policies ?

+ … or hard-to-justify ‘averaging’ assumption?

1

3

5 10

15%

20%

25%

30%

35%

40%

0.6

0.8

1

1.2

1.4

Maturity

IV

Strike

35%-40%

30%-35%

25%-30%

20%-25%

15%-20%

1

3

5 10

15%

20%

25%

30%

35%

40%

0.6

0.8

1.0

1.2

1.4

Maturity

IV

Strike

35%-40%

30%-35%

25%-30%

20%-25%

15%-20%

Equity volatility – richer model

12

Market Implied Volatility Surface ESG Generated IV Surface from

sophisticated model (SVJD)

+ Richer model provides simpler, easier to justify solution

1

3

5 10

15%

20%

25%

30%

35%

40%

0.6

0.8

1

1.2

1.4

Maturity

IV

Strike

35%-40%

30%-35%

25%-30%

20%-25%

15%-20%

1

3

5 10

15%

20%

25%

30%

35%

40%

0.6

0.8

1

1.2

1.4

Maturity

IV

Strike

35%-40%

30%-35%

25%-30%

20%-25%

15%-20%

P.6

ESG Economy Model Structure

13

+ Joint distribution – Correlation assumptions ensure plausible economic relationship across asset classes

Nominal short rate

Real short rate

Initial swap and government nominal

bonds

Index linked government bonds

Property Returns Alternative Asset Returns (eg commodities)

Credit risk model

Corporate Bond Returns Equity Returns Excess

returns (if any)

Exchange rate (PPP or Interest

rate parity)

Nominal minus real is inflation expectations

Realised Inflation and “alternative” inflation

rates (i.e Medical)

Real-economy; GDP and real wages

Foreign nominal short rate and

inflation

Macro economic variables

Risk factor distribution

+ Use joint distribution of financial risk factors to deduce income statement and balance sheet distribution

Example: Credit/Equity risk + E.g. asset price falls

should be associated with negative credit shocks

14 P.7

Global equity modeling example

+ Indices have exposure in different risk factors + Volatility of equities moves up and down together

– When vol goes up, correlation goes up too

15

“Global” Risk

Factor 1

Risk Factor

5

Risk Factor

4

Risk Factor

6

Risk Factor

3

Risk Factor

2

HK Equities

US Equities

Japan Equities

Sources of risk…

16

0

10

20

30

40

50

60

70

80

90

Nom

inal

Int.

Rat

es

Rea

l Int

. Rat

es

Exp

erie

nced

Infla

tion

Cre

dit

Dom

estic

Equ

ities

Ove

rsea

sEqu

ities

Pro

perty

Alte

rnat

ives

Cur

renc

y

Act

ive

Ris

k

Mor

talit

y

Tota

l div

ersi

ficat

ion

All

Ris

ks

Sources of Risk

Cha

nge

in S

urpl

us V

aR (£

m)

0

1

2

3

4

5

6Ex

pect

ed R

isk

Prem

ium

(£m

)

Interest rate & inflation risk

Equity risk Interaction of risk factors

Alternative investments

P.8

Applications

+ Specific consideration to applications

17

What it is for Consideration Calibration

(1) Liability valuation / pricing Estimate fair value of liability

� Valuation of options / guarantees

�MC

(2) Economic capital Assess level of resources required to withstand adverse scenarios

� Tail risk modeling �MC �RW

(3) Risk factor distribution Understand impact of market movements on company financials

� Relationship between each risk factor

�RW

(4) Strategic asset allocation Determine optimal asset strategies based on asset/liability portfolio

� Realistic assumption / distribution

� Alignment with risk metrics

�RW

Components of ESG model

18 P.9

Core components of ESG

+ Mathematical modelling: ESG Software – Research, develop, and maintain state of the art mathematical models

– Deliver these in an efficient, flexible, and user friendly format

+ Financial economic expertise and research: Model Calibration

– Market Consistent: Set up models to replicate observable market prices

– Real World: Set up models so that they produce realistic asset return behaviour

+ Documentation

– Communications and validation of results are important too!

19

Typical ESG modeling process

20

ESG/WSG £65m

Mathematical models

� � )()( 111 tZttrmr ������ �

Generate model

parameters specific to

application and market

conditions Market or historical

data

ESG - Calculation Engine

A series of mathematical models implemented in software

Calibration Content

� � )()( 111 tZttrmr ������ �

Output scenarios

Documentation covering the whole process

P.10

Calibration matters: Real-world vs Market-consistent

Real-world Market-consistent

Question to answer: What is the probability distribution of future asset prices?

What is the current market-consistent value of future cashflows?

Usage: Financial projections for ALM, cashflow testing, probability of ruin analysis

Fair valuation of liabilities (and Greeks)

Calibration: Calibrated to best-estimate targets

Calibrated to market option-implied volatilities

Risk premium: Y

N

21

A clarification of terminology…

Constructing the initial yield curve

22 P.11

Why does it matter

+ Interpolation – Discrete bond prices

from data vendor / brokers

– Methodology needed

to construct a full yield curve

+ Extrapolation

– Liquid trading for Government bonds usually up to medium terms

– Some limited freedom in constructing yield curve beyond this last liquid point

– More significant for firms with medium/long term products and low lapse rates

23

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

1.8%

0 5 10 15

Bon

d Yi

eld

Maturity

Yield from Fwd Spline

Market

Simple extrapolation for interest rate

+ USD government forward rates assuming constant rate beyond 30 years for 1985-2007:

+ Very conservative and will generate very high volatility in the MTM value of ultra long-term cash flows. – E.g. for TWD it would be at low levels for all maturities…

24

2%

3%

4%

5%

6%

7%

8%

9%

10%

11%

12%

0 10 20 30 40 50 60 70 80 90 100

Forw

ard

inte

rest

rate

Maturity (years)

P.12

Unconditional forward rate – an anchor

+ Unconditional ‘anchor’: stability in mark-to-model valuations

25

Extrapolating the curve

+ Two key assumptions in yield curve extrapolation – Ultimate forward rate (UFR): long term forward rate target

– Speed of mean reversion: how quickly long term rates reach UFR

26

0%

1%

2%

3%

4%

5%

6%

7%

0 20 40 60 80 100 120

Forw

ard

Rate

Maturity

Base Curve Shocked UFR Shocked Mean Reversion Speed

P.13

Exploring the impact on liability valuation + A typical example cashflow profile, assuming no options and

guranatees

27

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

HKD

Mill

ions

Cashflow

Sensitivities to assumptions

+ Comparison:

28

Discounted cashflow / GPV (Million)

Base (232)

Stressed down UFR 1,526

Stressed up mean reversion speed (5,922)

0%

1%

2%

3%

4%

5%

6%

7%

0 20 40 60 80 100 120

Forw

ard

Rate

Maturity

Base Curve Shocked UFR Shocked Mean Reversion Speed

+ Impact of rate level on cost of option is not included here

P.14

Liquidity premium

29

Liquidity premium

The basic idea: + Instruments with identical cash flows can sell at different prices

– Due to their trading liquidity => hard-to-trade instruments at a price discount

Implications for the valuation of illiquid liabilities: + MVL should treat illiquid cash flows consistent with market

The corporate bond spread can be decomposed as:

30 P.15

Approaches to LP estimation

+ LP is not observable directly so requires the use of estimation methods

+ Common approaches includes: – CDS negative basis method

– Covered bond method

– Structural model method

+ Each method has its issues due to data availability, assumptions made and reliance on well functioning markets

31

No single correct method: each method in isolation has advantages and disadvantages. However, results provide clear evidence of liquidity premium.

Example liquidity premium estimates

32

0

250

End Dec 2005 End Dec 2006 End Dec 2007 End Dec 2008 End Dec 2009

bps

Proxy Method GBPCovered Bond Method GBPCDS Negative Basis Method GBPStructural Model Method GBP

P.16

Liquidity premium in QIS 5

+ QIS 5 specified the use of liquidity premium (LP) adjustments for risk-free rates for valuing liabilities

+ The LP is defined using an approximate formula of the form: – LP = 0.5*(CreditSpread- 40bps)

+ Different proportions of the LP can be used depending on liability

nature

+ On-going discussion on matching premium

33

Using the same example

+ Comparison

34

0%

1%

2%

3%

4%

5%

6%

7%

0 20 40 60 80 100 120

Forw

ard

Rate

Maturity

Base Curve Shocked UFR Shocked Mean Reversion Speed Plus LP (30bps)

Discounted cashflow / GPV (Million)

Base (232)

Plus LP (say 30bps for 15 years) (2,075)

P.17

Mark-to-model in the absence of market prices

35

Cost of options and guarantees

+ Implied vol has a direct first order impact on option costs

36 P.18

Market-consistent liability valuation

+ Make reference to market implied vol data as far as possible + A common issue:

37

15%

20%

25%

30%

35%

0 5 10 15 20 25 30

Impl

ied

Vola

tilit

y

Maturity

Market IV

Liabilities

Is the market data enough?

+ Need to think beyond the objective world of market prices

+ Apply econometric analysis and expert judgment to fill in blanks

+ Economically robust, stable extrapolation key to stable, sensible valuation

+ For example, use a functional form to extrapolate vol to a stable unconditional estimate…

P.19

Example approaches

39

Constant Volatility

15%

20%

25%

30%

35%

0 5 10 15 20 25 30

Impl

ied

Vol

atili

ty

Maturity

Market IV

Model IV

Liabilities

Deterministic Volatility

15%

20%

25%

30%

35%

0 5 10 15 20 25 30

Impl

ied

Vol

atili

ty

Maturity

Market IV

Model IV

Liabilities

Functional Form Volatility

15%

20%

25%

30%

35%

0 5 10 15 20 25 30

Impl

ied

Vol

atili

ty

Maturity

Market IV

Model IV

Liabilities

Further thoughts…

+ Global trend in stochastic modeling – Sol II

– IFRS 4 phase 2

– Regional development: Japan, Mainland China, Australia, …

+ Capturing the values from stochastic models

– Wide applications

– Understanding of the model driving factors

+ The devil is in the details!

+ After the coffee break: workshop

40 P.20

Questions?

41

Workshop

42 P.21

Objective

+ Explore approaches to yield curve construction – Interpolation

– Extrapolation

+ Visualize how this affects PV of liabilities

Impact analysis

+ Assume we have a deterministic cashflow of USD 1 Million at end of year 60.

+ What is the PV of this cashflow?

P.22

Exercise

With “Yield Curve Construction Example.xls”:

+ Investigate the impact on PV of cashflow of: 1. Interpolation approach

2. Extrapolation approach

+ Fit each set of market data presented on the “Example_Data” tab.

– Which method gives the “best” fit in eachcase?

– Are the resulting yield curves realistic?

– Consider stability of fit with the time series data?

45

Get market data

+ How should we join the dots and what about extrapolation?

46 P.23

Approach for interpolation

An exact fit to all market data…

Or a functional form

47

Things to consider

+ Would we introduce unwanted volatility if we rely on market data solely?

+ How should we determine the functional form and parameters?

P.24

Approach for extrapolation

Constant forward rate Or a functional form

49

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

30 40 50 60 70 80 90 100 110 120

Forward Rate

Market Data

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

30 40 50 60 70 80 90 100 110 120

Forward Rate

Market Data

Things to consider

+ How should we determine – Mean reversion speed and ultimate forward rate?

+ Should interpolation and extrapolation have some form of smooth transition?

P.25

How PV is affected…

1%

10%

20%0

100,000

200,000

300,000

400,000

500,000

1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

Reversion speed

PV o

f cas

hflo

w

UFR

Extrapolation parameter sensitivities

0-100,000 100,000-200,000 200,000-300,000 300,000-400,000 400,000-500,000

Some final thoughts

+ Construction of initial yield curve looks superficially straightforward, but beware of the details

+ Projecting the yield curve is even more complicated, more so in a multi-asset multi-time period environment

+ Use of expert judgment is key

+ How should we document the decision making process and technical details of the whole calibration?

52 P.26

Thank you!

53

Copyright 2012 Barrie & Hibbert Limited All rights reserved. Reproduction in whole or in part is prohibited except by prior written permission of Barrie & Hibbert Limited (SC157210) registered in Scotland at 7 Exchange Crescent, Conference Square, Edinburgh EH3 8RD. The information in this document is believed to be correct but cannot be guaranteed. All opinions and estimates included in this document constitute our judgment as of the date indicated and are subject to change without notice. The products described in this report aid generic decisions and do not recommend any particular investment. As such, any opinions expressed do not constitute any form of advice (including legal, tax and/or investment advice). This document is intended for information purposes only and is not intended as an offer or recommendation to buy or sell securities. The Barrie & Hibbert group excludes all liability howsoever arising (other than liability which may not be limited or excluded at law) to any party for any loss resulting from any action taken as a result of the information provided in this document. The Barrie & Hibbert group, its clients and officers may have a position or engage in transactions in any of the securities mentioned. Barrie & Hibbert Inc. and Barrie & Hibbert Asia Limited (company number 1240846) are both wholly owned subsidiaries of Barrie & Hibbert Limited.

54 P.27