Understanding Risks In Structured Products

Dong Qu

December 2011, Scuola Normale Superiore - Pisa Table of Contents

1. Common Denominator in Structured Products Business

2. Key Risk Characteristics of Structured Products

3. Correlation vs. Contagion

2 1. Common Denominator in SP Business

. Structured product business pillars:

 Marketing/structuring;

 Trading/risk managing;  Quantitative modeling; . Marketing/structuring: provide products to meet investors’ financial needs & risk appetites;

. Trading/risk managing: hedge & mitigate risks;

. Quantitative modeling: develop quantitative models to price the cost of hedging risks;

3 Risk is the Common Denominator

Capital Return Risks

Growth Option Risks Secured Linked to Markets Products (Impact Return)

Income Not Much Enhanced Option Risks Products Secured Yield/Income (Impact Capital)

CPPI Protected But Gap Risks Linked to Markets (Fund) Not Secured (Impact Both)

4 Quantitative Models

. Quantitative models: mathematical tools to price the Risks and their hedging costs;

. Good quantitative models:

 Able to calibrate to the markets properly;

 Able to capture key risk exposures;

 Numerically stable for pricing;

 Numerically stable for generating Greeks;

 Computationally efficient.

5 2. Key Risk Characteristics of Structured Products

. Partial Differential Equation (PDE): V V 1 2V Sqr   S 22   Vr t S 2 S 2

. Risks Embedded in Options:

 Time decay – Theta;

 Spot – Delta;

 Spot – Gamma;

 Volatility – Vega;

 Rate – Rho.

6 “Exotic”Risks

. “Exotic” Risks Embedded in Options:

 Dividend Risk;

 Quanto Risk;

 Volatility Skew/Smile Risk;

 Gap Risk;

 Hybrid Risk;

 Correlation Risk.

7 Risks That Supposed to be Trivial

. Dividend Risk:

 Most banks use deterministic sets of forecast dividends in pricing models;

 During 2008 crises, banks had to mark down the dividends, resulted in substantial losses;

. Quanto Risk:

 Most banks use the simple quanto adjustment;

 Again, during 2008 crises, banks’ equity positions lost lots of money on quanto (FX) exposures.

8 Quanto Hedge Becomes Difficult …

. Both equity and FX vol shoot up;

. Correlation shoots up;

. Stochastic vol effect becomes significant;

. FX smile comes into play.

Risks that supposed to be insignificant became Massive!

9 40 Volatility Skew/Smile Risk

4700

DJ_STOXX50 Spot vs ImpVol 30 Spot ImpVol 4300

20

3900

10 02/07/2007 26/08/2007 20/10/2007 14/12/2007 07/02/2008

3500

. When market crashes, volatility shoots up!

10 Delta in the Presence of Skew

. Equity skew effectively illustrates the correlation between Spot and Volatility;

. Option delta is a function of skew:  V  V       S    S . Skew dynamics:

 Sticky delta (ATM vol moves with spot);

 Sticky strike (Black-Scholes delta);

 Sticky local vol (Static local vol, e.g. in PDE);

11 Delta Hedge Under Skew Dynamics

. Re-writing option delta:

V V     S  S  BS vegaBS   tL )( S Surface

. Delta under skew dynamics:

 L(t) = -1, sticky delta, real delta > BS delta;

 L(t) = 0, sticky strike, real delta = BS delta;

 L(t) = 1, sticky local vol, real delta < BS delta;

12 Delta Under Skew Dynamics (CALL)

Delta vs Maturity (European Call)

90% L = -1 80% L = -0.5 70% L = 0 60% L = 0.5

50% L = 1

40%

30%

Maturity 012345

13 Delta Under Skew Dynamics (PUT)

Delta vs Maturity (European Put)

0% L = -1 -10% L = -0.5 -20% L = 0

-30% L = 0.5 L = 1 -40%

-50%

-60%

Maturity 012345

14 An Example of L(t) Term Structure

L(t) Term Structure 0%

-25%

-50%

-75%

-100% 0246810 Years

15 Skew Risks in Illiquid Markets

. Skew risks are real:

 Skew represents spot-vol correlation;

 When market moves, volatility moves too!

. In illiquid markets (e.g. emerging markets):

 Option quotes are scarce, even for ATM;

 Very difficult to obtain implied vols at various strikes;

 Very little market information on volatility skew;

 But the skew risks STILL exist and are REAL!

16 Gap Risks in CPPI

. CPPI uses GC measure to dynamically re-balance risky assets (e.g. shares) and risk free assets (e.g. cash);

. Gap Condition (GC): T  DFGVGC tTt

. Gap Condition is simply the gap between the current fund value and promised guarantee (pv_ed);

. It is effectively an investment safety buffer.

17 CPPI - Dynamic Re-balance

. Switching between risky and risk free assets:

 If GC is large (e.g. > 25% Of Gt ), whole fund will be invested in risky assets, to fully benefit from market upside;

 If GC is zero (i.e. Vt = Gt), whole fund will be invested in cash, to fulfil the promised guarantee;

 Between the two extreme cases, a portion will be invested in risky assets, with the remaining in risk free asset. The asset re-balance is conducted dynamically.

18 An Example CPPI Path

CPPI Return vs Equity Path 150% Equity Path 125% CPPI Return

100%

75%

50%

25%

0% 012345

19 Gap Risk

Risky Investment Proportion vs Gap Condition

40%

20%

0%

-10% -5% 0% 5% 10%

20 Hybrid Risks

. Equity Linked GAO: pension & insurance products, equity + interest rate + correlation risks:

T  0  max( T  KSNN )0,

TT  T grNA ),max(

. Equity & Debt Products: convertible bonds, equity + credit + correlation risks:

V V 1 2V CB Sqr  CB  S 22  CB )(  VScVr t S 2 S 2 CB B

21 3. Correlation vs. Contagion

. Stock markets correlation: global economy;

. Credit markets correlation: global economy;

. Stock/FX correlation: when markets are in distress;

. Credit/FX correlation: there have always been strong links between emerging markets FX and

sovereign credits;

. Since credit crunch, many countries behave like emerging markets as far as credit is concerned.

22 Stock Markets Correlation

Stock Markets (China, Europe, USA) 1600 6000 SHCOMP SX5E 1400 5000 SPX

1200 4000

1000 3000

800 2000

600 1000 01/01/2008 08/12/2008 15/11/2009 23/10/2010 30/09/2011

23 Credit Markets Correlation

Credit Default Swap 1200

GERMANY ITALY 900 Morgan Stanley

600

300

0 01/01/2008 08/12/2008 15/11/2009 23/10/2010 30/09/2011

24 Stock & FX Correlation

1.7 4500 Stock & FX Correlation

SX5E 1.6 4000 EURUSD

1.5 3500

1.4 3000

1.3 2500

1.2 2000

1.1 1500 01/01/2008 08/12/2008 15/11/2009 23/10/2010 30/09/2011

25 Credit & FX Correlation

Credit & FX Correlation 500 1.7

ITALY EURUSD 400

1.5

300

200 1.3

100

0 1.1 01/01/2008 08/12/2008 15/11/2009 23/10/2010 30/09/2011

26 UK - CDS vs. FX (Credit Crunch)

During Crunch: UK (FX vs CDS)

200 2.0 CDS GBPUSD

160 1.8

120

1.6

80

1.4 40

1.2 0 08/08/2008 03/11/2008 29/01/2009 26/04/2009 22/07/2009

27 What Happened In 2008?

. Collateralized Debt Obligation (CDO): a pool of assets, with defined tranches of credit loss;

 Each tranche can be sold to investors to suit their risk appetites;

 The pool as a whole has no correlation risk, but pricing any single tranche CDO (STCDO) involves pricing in correlation risks;

. One needs to model joint default risks (correlation);

. Copula was used to model the joint default risks.

28 Sub-Prime Distribution Mechanism

Domestic Investors RMBS CDO (Sub-Prime) Tranches Foreign Investors Banks (Pricing Model)

. All elements were in place! Ready to go!

29 CDO Lessons

. There was a false sense of security – “we can now value CDOs”. The world had since sold far too much of them!

. Simply because ones can value CDOs, it does NOT mean they can practically risk manage CDOs:

 Hedging difficulties;  Over leveraging problems;  Correlation assumptions;  Liquidity issues;  Transparency & visibility issues;  Etc.

30 What Is Happening Now (2011/2012)?

. Instead of sub-prime mortgages in USA, it’s now sovereign debts in Europe;

. Very high Debt to GDP Ratio: Greece (143%), Italy (119%), etc;

. In addition, GDP does not grow but decline;

. Faced with huge contagion risks, let’s hope politians find answers very very soon;

. In fact, the contagion risks are surprisingly similar to basket correlation risks!

31 Basket Options* Analogy

. Basket correlation risks:

 Cross Gamma: one underlying can affect the others;

 Correlation risk: co-dependence can change;

 Correlation skew risk: when markets fall, correlation shoots up;

 Credit default risk: basket underlying can go bust;

* Qu, D. (2005), “Pricing Basket Options With Skew”, Wilmott Magazine, July

32 Contagion Risks

. Contagion Risks: versus basket correlation risks:

 Cross Gamma: one country can affect the others;

 Correlation risk: co-dependence can change;

 Correlation skew risk: when in crisis, countries’ co-dependency becomes much stronger, hence

increases chance of “getting worse together”;

 Credit default risk: a country can default.

33 Basket Correlation  Contagion

The World Is Like A Correlated Basket !!

Questions?

34