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**Emerging Markets Derivatives**

Vladimir Finkelstein JPMorgan

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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

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**Volatility of Credit Spreads**

JPMorgan

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**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 JPMorgan

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**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

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**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 JPMorgan

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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 JPMorgan

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**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 JPMorgan

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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

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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 JPMorgan

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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. 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

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**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

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**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

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**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

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**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 JPMorgan

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