1. Emerging Markets Derivatives
Vladimir Finkelstein
JPMorgan

2. 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)
JPMorgan

3. Volatility of Credit Spreads
JPMorgan

4. Benchmark Curves for a Given Name
Default-free Discounting Curve (PV of $1 paid with certainty)
Clean Risky Discounting Curve [CRDC] (PV of $1 paid contingent on no default till maturity, otherwise zero)
has a meaning of instantaneous probability of default at time τ
where is a forward probability of
default
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5. Credit Default Swap JPM XYZ JPM XYZ
A basic credit derivatives instrument: JPM is long default protection
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
JPM
XYZ
conditional on no default of a reference name
JPM
XYZ
conditional on default of a reference name
JPMorgan

6. Pricing CDS PV of CDS is given by
Assume , and no correlation of R with spreads and interest rates
As Eq (1) is linear in R, CRDC just depends on expected value , 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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7. Generating CRDC
A term structure of par credit spreads is given by the market
To generate CRDC we need to price both legs of a swap
No Default (fee) leg
Default leg
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8. Correlation Adjustment
Need to take into account correlation between spreads and interest rates to calculate adjusted forward spread
Default-free rate conditional
on no default also needs to be
adjusted as \
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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9. 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
Bond price goes to R in default
No generic risky zero coupon bonds with non zero recovery
JPMorgan

10. 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
JPMorgan

11. 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.
where
and are forward and spot FX rates ($ per foreign currency),
is the (market) risk-free foreign currency zero coupon bond
maturing at T,
is the discount factor representing the probability of no default
in (0,T) in foreign currency.
JPMorgan

12. 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 , under no default conditions the foreign currency should have an excessive return in terms of DC given by to compensate for a possible loss in value
Consider a FC clean risky zero coupon bond (R=0)
is an excessive return in FC that compensates for a possible default
The position value in DC = (Bond Price in FC) * (Price of FC in DC)
An excessive return of the position in DC is
The position should have the same excessive return as any other risky bond in DC which is given by
To avoid arbitrage the FC credit spread should be
An adjustment can be big
JPMorgan

13. 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
JPMorgan

14. Quanto Adjustment (cont’d)
Adjustment for a DC flat spread curve of 600 bp. Spread MR is important
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.
JPMorgan

15. Quanto Adjustment (cont’d)
Assumptions on spread distribution are important
Difference between normal and log-normal adjustment decreases as mean reversion is increased for constant spot volatility
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