Emerging Markets Derivatives
Vladimir Finkelstein
JPMorgan
1
EM Derivatives
• EM
-
-
provide stress-testing for pricing and risk management techniques
High spreads: from 100 bp to “the sky is the limit” (e.g. Ecuador 5000bp)
High spread volatility: from 40% up to 300%
Default is not a theoretical possibility but a fact of life (Russia, Ecuador )
Risk management with a lack of liquidity:
short end of the yield curve Vs. long end
gap risk
Reasonably deep cash market with a variety of bonds
Two-way Credit Default Swap market
Traded volatility (mostly short maturities)
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2
0.00%
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01/15/1999
09/30/1998
06/15/1998
02/26/1998
11/11/97
07/25/1997
04/09/97
12/23/1996
09/05/96
05/21/1996
02/02/96
10/18/1995
07/03/95
03/16/1995
11/29/1994
08/12/94
04/27/1994
01/10/94
09/23/1993
06/08/93
02/19/1993
11/04/92
07/20/1992
Volatility of Credit Spreads
Argentina FRB Stripped Spread
25.00%
20.00%
15.00%
10.00%
5.00%
3
Benchmark Curves for a Given Name
• Default-free Discounting Curve (PV of $1 paid with certainty)
t
t






def  free
Z
(0, t )  E0 exp    r d   exp    rˆ d 
  0

 0

• Clean Risky Discounting Curve [CRDC] (PV of $1 paid contingent on no
default till maturity, otherwise zero)
t



risky
Z (0, t )  E0 exp    (r  s )d 
  0

s
has a meaning of instantaneous probability of default at time τ
Z risky (0, t )  Z def  free (0, t )  PND (0, t )
 t

PND (0, t )  exp    sˆ d  where ŝ
 0
 default
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is a forward probability of
4
Credit Default Swap
• A basic credit derivatives instrument: JPM is long default protection
JPM
S Dpar with frequency 
XYZ
conditional on no default of a reference name
1 R  S
JPM
par
  accr
XYZ
conditional on default of a reference name
• R is a recovery value of a reference bond
• Reference bond:
no guarantied cash flows
cheapest-to-deliver
cross-default (cross-acceleration)
• Same recovery value R for all CDS on a given name
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Pricing CDS
• PV of CDS is given by
T   r  s d 
T

   r  s d
  ST E0   e 0
dt   E0   (1  Rt ) st e 0
dt  (1)
0

0





t
PVCDS
t
• Assume Rt  R, R  E ( R) , and no correlation of R with spreads and
interest rates
• As Eq (1) is linear in R, CRDC just depends on expected value R , not on
distribution of R
• Put PV of CDS = 0, and bootstrapping allows us to generate a clean risky
discounting curve
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6
Generating CRDC
• A term structure of par credit spreads S
is given by the market
T , par
• To generate CRDC we need to price both legs of a swap
• No Default (fee) leg
T   r  s d 
T
ST , par E0   e 0
dt   ST , par  Z risky (0, t )dt
0

0


t
• Default leg
T

T   r  s d 
T
   r  s d
~ risky




0
0
E0  (1  Rt ) st e
dt  (1  R ) E0  st e
dt  (1 - R )  sˆt Z (0, t )dt
0

0

0




t
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t
7
Correlation Adjustment
• Need to take into account correlation between spreads and interest rates to
calculate adjusted forward spread
~
sˆ  sˆ  Adjs
~
Default-free rate rˆ conditional
Spread and Rate Adjustments Vs. Maturity
\
30
27
25
22
20
17
15
12
10
7.
5
2.
Rate Adj
0
0.005
0.004
0.003
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
-0.005
Vols=80%,Volr=20%,MRs=0.5,MRr=0.05,Corr=0.3, S=6%,r=5%
Spread Adj
on no default also needs to be
adjusted as
~ ~
sˆ  rˆ  sˆ  rˆ
~
rˆ  rˆ  Adjs
• For high spreads and high volatilities an adjustment is not negligible
• For given par spreads forward spreads decrease with increasing volatility,
correlation and level of interest rates and par spreads
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8
Recovery Value
• For EM bonds a default claim is (Principal+Accrued Interest) , that is
recovery value has very little sensitivity to a structure of bond cash flows
• The price of a generic bond can be represented as
B(t ,t N )   Cn Z
risky
(t , t n )  Z
risky
(t , t N )
n

 R 1   Ln1Z
 n
risky
(t , tn )  Z
risky

(t , t N )

• Bond price goes to R in default
• No generic risky zero coupon bonds with non zero recovery
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More on Recovery Value
• Other ways to model recovery value
- Recovery of Market Value (Duffie-Singelton) :
Default claim is a traded price just before the event
- Recovery of Face Value :
For a zero coupon bond default claim is a face value at maturity
( PV of a default-free zero coupon bond at the moment of default)
- Both methods operate with risky zero coupon bonds with embedded
recovery values. One can use conventional bond math for risky bonds
- Both methods are not applicable in real markets
• Implications for pricing off-market deals, synthetic instruments, risk
management
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Pricing Default in Foreign Currency
• As clean forward spreads represent implied default probabilities they should
stay the same in a foreign currency (no correlation adjustments yet)
• Due to the correlation between default spread and each of FX, dollar interest
rates, and foreign interest rates, the clean default spread in a foreign currency
will differ from that expressed in dollars.

 T F 
 T
 
1
P (0, T )  exp   sˆ d   E0  X T exp   s  r d   
def  free
(0, T )

 0

 0
  X 0 Z F
F
ND
•
•
where
X T and
X 0 are forward and spot FX rates ($ per foreign currency),
Z Frisky (0, T ) is the (market) risk-free foreign currency zero coupon bond
maturing at T,
F
P
• ND (0, T ) is the discount factor representing the probability of no default
in (0,T) in foreign currency.
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11
Adjustment for FX jump conditional
on RN Default
• FX rate jumps by -α % when RN default occurs (e.g. devaluation)
• As probability of default (and FX jump) is given by t , under no default
conditions the foreign currency should have an excessive return in terms of DC
given by st   to compensate for a possible loss in value
• Consider a FC clean risky zero coupon bond (R=0)
F
is an excessive return in FC that compensates for a possible default
t
The position value in DC = (Bond Price in FC) * (Price of FC in DC)
• An excessive return of the position in DC is S   S F
t
t
• The position should have the same excessive return as any other risky bond in
DC which is given by
t
• To avoid arbitrage the FC credit spread should be
s
s
s
StF  St  (1   )
• An adjustment can be big
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12
Quanto Spread Adjustment
• In the no default state correlation between FX rate and interest rates on one
side and the credit spread on another results in a quanto adjustment to the
credit spread curve used to price a synthetic note in FC
• Consider hedges for a short position in a synthetic risky bond in FC
- sell default protection in DC
- long FC, short DC
• If DC strengthens as spreads widen (or default occurs ) we would need to
buy back some default protection in order to hedge the note and sell the
foreign currency that depreciated.
• Our P&L would suffer and we would need to pass this additional expense to
a counter party in a form of a negative credit spread adjustment
• For high correlation the adjustment can be significant
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Quanto Adjustment (cont’d)
• Adjustment for a DC flat spread curve of 600 bp. Spread MR is important
Effect of Mean Reversion on Log-Normal Spread
Adjustment
0
Spr -50
ead
Adj -100
ust
me -150
nt
(bp -200
)
-250
Mean Reversion
0
0.2
0.5
1
-300
-350
1
2
3
4
5
6
7
8
9
10
11
12
Year
•
Spread adjustment decreases with increasing mean reversion and constant spot volatility. α =0.2, S=6%,
r$=5%, rf=20%, s=80%, $=12.5%, $= 0, f=40%, s=0.5, x=20%, $s=0, fs=0.5, xs=0.7. All curves are
flat.
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Quanto Adjustment (cont’d)
• Assumptions on spread distribution are important
Difference of Normal and Log-Normal Spread Adjustments
Adjustment Difference (N-LN) (bp)
0
-50
Mean Reversion
0
-100
0.2
-150
0.5
-200
1
-250
-300
1
2
3
4
5
6
7
8
9
10
11
12
Year
•
Difference between normal and log-normal adjustment decreases as mean
reversion is increased for constant spot volatility
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