Understanding Risks In Structured...
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Understanding RisksIn Structured Products
Dong Qu
December 2011, Scuola Normale Superiore - Pisa
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Table of Contents
1. Common Denominator in Structured Products Business
2. Key Risk Characteristics of Structured Products
3. Correlation vs. Contagion
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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;
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Risk is the Common Denominator
Capital Return Risks
Growth Products Secured Linked to Markets Option Risks
(Impact Return)
Income Products
Not Secured
Much Enhanced Yield/Income
Option Risks (Impact Capital)
CPPI(Fund)
Protected But Not Secured Linked to Markets Gap Risks
(Impact Both)
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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.
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2. Key Risk Characteristics of Structured Products
Partial Differential Equation (PDE):
Risks Embedded in Options:
Time decay – Theta;
Spot – Delta;
Spot – Gamma;
Volatility – Vega;
Rate – Rho.
VrSVS
SVSqr
tV
2
222
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“Exotic” Risks Embedded in Options:
Dividend Risk;
Quanto Risk;
Volatility Skew/Smile Risk;
Gap Risk;
Hybrid Risk;
Correlation Risk.
“Exotic” Risks
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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.
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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!
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When market crashes, volatility shoots up!
DJ_STOXX50 Spot vs ImpVol
3500
3900
4300
4700
02/07/2007 26/08/2007 20/10/2007 14/12/2007 07/02/200810
20
30
40SpotImpVol
Volatility Skew/Smile Risk
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Delta in the Presence of Skew
Equity skew effectively illustrates the correlation between Spot and Volatility;
Option delta is a function of skew:
Skew dynamics:
Sticky delta (ATM vol moves with spot);
Sticky strike (Black-Scholes delta);
Sticky local vol (Static local vol, e.g. in PDE);
SV
SV
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Re-writing option delta:
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;
)(tLS
vega
SV
SV
SurfaceBSBS
Delta Hedge Under Skew Dynamics
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Delta Under Skew Dynamics (CALL)
Delta vs Maturity (European Call)
30%
40%
50%
60%
70%
80%
90%
0 1 2 3 4 5Maturity
L = -1L = -0.5L = 0L = 0.5L = 1
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Delta Under Skew Dynamics (PUT)
Delta vs Maturity (European Put)
-60%
-50%
-40%
-30%
-20%
-10%
0%
0 1 2 3 4 5Maturity
L = -1L = -0.5L = 0L = 0.5L = 1
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An Example of L(t) Term Structure
L(t) Term Structure
-100%
-75%
-50%
-25%
0%
0 2 4 6 8 10Years
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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!
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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 ):
Gap Condition is simply the gap between the current fund value and promised guarantee (pv_ed);
It is effectively an investment safety buffer.
TtTt DFGVGC
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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.
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An Example CPPI Path
CPPI Return vs Equity Path
0%
25%
50%
75%
100%
125%
150%
0 1 2 3 4 5
Equity PathCPPI Return
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Gap Risk
Risky Investment Proportion vs Gap Condition
0%
20%
40%
-10% -5% 0% 5% 10%
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Hybrid Risks
Equity Linked GAO: pension & insurance products, equity + interest rate + correlation risks:
Equity & Debt Products: convertible bonds, equity + credit + correlation risks:
),max()0,max(0
grNAKSNN
TTT
TT
BCBCBCBCB VScVr
SVS
SVSqr
tV
)(
21
2
222
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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.
3. Correlation vs. Contagion
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Stock Markets Correlation
Stock Markets (China, Europe, USA)
1000
2000
3000
4000
5000
6000
01/01/2008 08/12/2008 15/11/2009 23/10/2010 30/09/2011600
800
1000
1200
1400
1600SHCOMPSX5ESPX
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Credit Markets Correlation
Credit Default Swap
0
300
600
900
1200
01/01/2008 08/12/2008 15/11/2009 23/10/2010 30/09/2011
GERMANY
ITALY
Morgan Stanley
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Stock & FX Correlation
Stock & FX Correlation
1500
2000
2500
3000
3500
4000
4500
01/01/2008 08/12/2008 15/11/2009 23/10/2010 30/09/20111.1
1.2
1.3
1.4
1.5
1.6
1.7
SX5EEURUSD
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Credit & FX Correlation
Credit & FX Correlation
0
100
200
300
400
500
01/01/2008 08/12/2008 15/11/2009 23/10/2010 30/09/20111.1
1.3
1.5
1.7
ITALY
EURUSD
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UK - CDS vs. FX (Credit Crunch)
During Crunch: UK (FX vs CDS)
0
40
80
120
160
200
08/08/2008 03/11/2008 29/01/2009 26/04/2009 22/07/20091.2
1.4
1.6
1.8
2.0CDSGBPUSD
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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.
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Sub-Prime Distribution Mechanism
All elements were in place! Ready to go!
RMBS
(Sub-Prime)CDO
Tranches
Domestic Investors
Banks
(Pricing Model)
Foreign Investors
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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.
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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!
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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
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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.
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Basket Correlation Contagion
The World Is Like A Correlated Basket !!
Questions?