JPMorgan

1
Emerging Markets Derivatives

• Vladimir Finkelstein

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)

3
Volatility of Credit Spreads
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 t
• 
  
• 
  where is a forward
  probability of
• 
  default

5
Credit Default Swap

• 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
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

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

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

9
Recovery Value

• For EM bonds a default claim is
  (PrincipalAccrued 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

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

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.

12
Adjustment for FX jump conditional on RN Default

• FX rate jumps by -a 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 (R0)
  
• 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

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 PL 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

14
Quanto Adjustment (contd)

• 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. a
  0.2, S6, r5, rf20, ?s80, ?12.5, ?
  0, ?f40, ?s0.5, ?x20, ?s0, ?fs0.5,
  ?xs0.7. All curves are flat.

15
Quanto Adjustment (contd)

• Assumptions on spread distribution are important
• Difference between normal and log-normal
  adjustment decreases as mean reversion is
  increased for constant spot volatility