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Synthetic Credit Options
Trading Credit Risk and Credit Volatility via Options
March 2012
Abel ElizaldeAC
Credit Derivatives and Quantitative Credit Research
J.P. Morgan Securities Ltd
+44(0) 20 7742 7829
This presentation was prepared exclusively for instructional purposes only, it is for your information only. Itis not intended as investment research. Please refer to disclaimers at back of presentation.
Synthetic Credit Options
Trading Credit Risk and Credit Volatility via Options
Payer and receiver options
Definition, payoffs & mechanics
O tion cost and breakeven s reads
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Pricing
Expressing spread and volatility views using credit options
Volatility
Implied vs. realised, term structure & skew
Option to buy/sell protection at a future date at an agreed spread
Options on CDS Indices (iTraxx Europe, Crossover, Financials, CDX IG) and Single Name
CDS (less liquid).
Main features:
European style: only exercisable at expiry.
Options on Credit Derivatives
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5 year underlying CDS.
Most liquidity in volatile underlyings, e.g. iTraxx Crossover index
Liquid maturities: 3, 6, 9 months
Strike is quoted in a full running format.
Well focus on the mechanics & pricing of options on single name CDS. Options on CDSindices work in a similar way except for a few differences that we will highlight.
Receiver
Right to sell protection, i.e. put option on CDS spread
Payer:
Right to buy protection, i.e. call option on CDS spread
Receiver & Payer Options
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Alternatives:
Buy receiver option: buy the right to sell protection
Sell receiver option: sell the right to sell protection
Buy payer option: buy the right to buy protection
Sell payer option: sell the right to buy protection
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Payer Options Payoff
Buy Payer Option
300
400
500
5,0
5,5
6,0
Payoff = (Spread Strike)*DVO1 Premium
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-100
0
100
0 25 50 75 100 125 150 175 200
3,0
3,5
4,0
,
Payof f (LHS) DVO1 (RHS)
ecreases
with spread
Source: J.P. Morgan.
Receiver & Payer Exposure
Buy payer Sell Payer Buy Receiver Sell Receiver
Buy Sell Buy Sell
Right to Buy protection Buy protection Sell protection Sell protection
Spread exposure Short Long Long Short
Spread Vol. Expoure Long Short Long Short
Credit (risk) exposure
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Risk factors
Spreads
Spread volatility
Interest rates
Default of the underlying
What happens to the option contract if the underlying defaults before the optionexpiry?
Source: J.P. Morgan.
The option contract can:
Knock-Out
Option is terminated at the time of default: no payments, no exercise.
No Knock-Out
Knock-Out and No Knock-Out
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The option buyer has the right to exercise the option. The option gives theright to buy or sell protection in a credit which has defaulted. Buyers of payeroptions will exercise, buyers of receivers will not
When is the option exercised? Two possible cases:
Now (i.e. at the time of default): Option acceleration
At option expiry: No acceleration
What is the impact of knock-out in an option premium?
Payer option:
More expensive without Knock-Out
It would always be profitable to exercise a payer option on a defaulted name
(You would be buying protection, at a fixed spread, on a defaulted name;
Upon Default
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receiving 1 Recovery)
Receiver option:
No price impact
Upon default, you would never exercise a receiver option
(You do not want to sell protection, at a fixed spread, on a defaulted name)
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Assume you buy a payer option with notional 1 and expiry T
Knock-out option
Scenario 1: No default .
Scenario 2: Default before expiry ..
No Knock-out option (no acceleration)
Payer options: More expensive without Knock-Out
]0,1)max[(TT
DVOKS
0
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Scenario 1: No default .
Scenario 2: Default before expiry ..
In the No Knock-Out case the payoff is equal or better; thus, its price must be higher
Repeat this exercise for a receiver option and show that, in that case, the payoffs of aKnock-Out and No Knock-Out options are the same no matter whether there is a defaultor not.
]0,1)max[( TT DVOKS
01]0,1max[ >= RR
Consider a single name CDS option, What will be more expensive?
Payer option, No knock-out, with acceleration.
Payer option, No knock-out, without acceleration.
Repeat the exercise of the previous slide considering the two alternatives above.
Payer options with No Knock-Out
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Single name options are generally traded with Knock-Out
Index options are generally traded with No Knock-Out (and No Acceleration)
What happens in an index option if there is a default before the expiry?
Knock-Out and No Knock-Out: Single name vs. Index options
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Will the buyer of payer index options always exercise if there has been one default?
Expressing a bullish view on spreads
Sellindex
protection
Simplest strategy to take a view on
spread tightening
Linear return profile if spreads widen ortighten
Unlimited downside risk if spreads widen20bp 50bp 80bp
er
Limit downside risk by buying a receiveroption
Decreasing priceIncreasing spreads
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BuyRecei
Full upside in spread tightening (minus
premium)20bp 50bp 80bp
SellPay
er
Bullish view if believe spreads will
tighten but not past x
Strategy outperforms selling indexprotection for levels above x
20bp 50bp 80bpX
Decreasing priceIncreasing spreads
Decreasing priceIncreasing spreads
Source: J.P. Morgan.
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Expressing a bearish view on spreads
Bu
yindex
protection
r
Simplest strategy to take a view onspread widening
Linear return profile if spreads widen or
tighten
Downside risk capped as spreads cannotbe negative
20bp 50bp 80bp
Limit downside risk by buying a payeroption
Decreasing priceIncreasing spreads
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BuyPaye
SellReceiver
Full upside in spread widening (minus
premium)
Maximum loss limited to premium paid
for option
20bp 50bp 80bp
Bearish view if believe spreads will widenbut not past x
Strategy outperforms buying index
protection for levels below x20bp 50bp 80bpX
Decreasing priceIncreasing spreads
Decreasing priceIncreasing spreads
Source: J.P. Morgan.
Assuming there is no default, the breakeven spread of an option is the spread for the
underlying at the option expiry which generates a total PnL equal to zero.
For a payer option:
Breakeven Spreads
KCost
S
CostDVOKSCDS
TP
TTTP
+=
=
*
,
*01]0),max[(
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For a receiver option:
We use the forward DVO1 to compute the expected breakeven spread
DVOCDSTT,
1
CDS
CDS
TT
TR
TTTR
DVO
CostKS
CostDVOSK
,
*
,
*
1
01]0),max[(
=
=
We are concerned about a spread widening and want to buy protection using options(9-Mar-09)
We choose to buy an OTM (1300bp Strike) Payer on 5y iTraxx Crossover on $10,000,000notional
Cost (Premium) of the option is quoted at 392c in the market, for a Jun 20th 2009 expiry
Current spread on iTraxx Crossover is 1150bp
A Simple Example Entering the Options Contract
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This means we are buying the option (right) to buy iTraxx Crossover protection (short risk)at 1300bp on $10,000,000 notional on Jun 20th
Costs
We have to pay 392c on $10,000,000 notional to
enter the contract
Cost = (392/10000) * $10,000,000 = $392,000
Option P+L at Expiry
1000bp 1300bp 1600bp
Buy Payer
iTraxx CrossoverSpreads
Source: J.P. Morgan.
Breakevens
We will be buying protection at 1300bp, so at first thought if spreads are above1300bp at expiry well make money
But, as we saw, the cost of the option was 392c
So, we need the index to widen more than 1300bp to make-up for the cost
A Simple Example - Breakevens
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We nee to in t e rea even sprea at expiry
Option P+L at Expiry
1000bp 1300bp 1600bp
Buy Payer
iTraxx CrossoverSpreads
Breakeven Spread
Source: J.P. Morgan.
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Modelling Single-Name and Multi-Name Credit Derivatives D. OKane. 2008.
Chp. 9: Forwards, Swaptions and CMDS, and references therein.
Here, we outline the pricing of options on single name CDS. However, most of theliquidity is around options on CDS indices. For details on the pricing of CDS index options
see:
References on CDS Option pricing
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Chp. 11: Options on CDS Portfolio Indices, and references therein.
Options on CDS indices do not knock-out and do not accelerate.
Compared to single name CDS options, the pricing of options on CDS indices should
take into account the fact that the index does not disappear even if somecredits default.
Consider the case of a knock-out single name CDS option
Payer payoff at maturity:
Receiver payoff at maturity:
Pricing: Option Payoffs
]0,1)max[( TT DVOKSPO =
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Where is the CDS spread at option expiry T, is the option strike, and
is the CDS DVO1 at expiry T
K
TDVO1
TS
]0,1)max[( TT DVOSKRO =
If default happens before option expiry, will be zero
Assuming the CDS spread follows a Geometric Brownian Motion, one can apply the
Black-Scholes machinery for option pricing
Modified Black-Scholes
TDVO1
No Exam
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TT DVOSKRO 1]0),max[( =
TTDVOKSPO 1]0),max[( =
Equity call payoff at expiry
where Tis the option maturity, S is the stock price, and C is the call option price.
(equities, i.e. the underlying, do not have a maturity; however, CDS do!)
Black-Scholes for Equity Options
]0),max[( KSC TT =
No Exam
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Assume risk neutrality and equity price follows a Geometric Brownian Motion
where is the interest rate, the volatility and a Browniam MotiontWr
tttt dWSdtrSdS +=
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Call price
(Today 0, expiry T)
Black-Scholes for Equity Options
dNeKdNSC
rT
rT
=
2100 )()(
No Exam
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TddT
TKSEd
eSSE
T
rT
T
T
=
+=
=
=
12
2
1
0
21
;2/)/][ln(
][
Using a similar derivation than for equity options
Payer price (Today 0, option expiry T, underlying CDS maturity TCDS)
Black-Scholes for CDS Options
DVOdNKdNFP CDSCDS TTTT = ,21,0 1)]()([
No Exam
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FT,TCDS and DVO1T,TCDS are the forward spread and duration of a CDS contract starting at T
and maturing at TCDS.
We can compute them using an arbitrage argument and the spread and durations of CDS
contracts which start today and mature at Tand TCDS
TddT
TKFd CDS
TT
=+
=12
,
1;
2/)/ln(
Payer and receiver option prices (with knock-out)
Black-Scholes for CDS Options
CDSCDS TTTT
DVOdNFdNKR
DVOdNKdNFP ,21,0
1
1)]()([
=
=
No Exam
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What if the option does not knock-out?
Receiver does not change
Payer should be more expensive
What is the value added of the No Knock-Out in a payer option?
CDSCDS ,,
As we argued before, the holder of a receiver option will never exercise it if the CDS has
defaulted since it would result in a loss.
For a payer option:
Value of No-Knock Out Payer = Value of Knock-Out Payer + Value of No-Knock OutFeature
Payer & No Knock-Out
No Exam
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If there is no default, the No-Knock-Out feature does not kick in
In case of default, the buyer of the payer receives (1 Recovery)
At the time of default, if the option accelerates
At option expiry, if the option does not accelerate
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N E N E
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No Exam
Selling Credit Volatility Three Variations
Selling credit volatility is most successful after a sell-off dueto the high spread levels and high implied volatilitiespushing up the price of straddles; the two most successful
periods for this strategy has been the months following
Lehmans collapse in 2008 and 2H11.
Jumps in realised volatility normally c ause a short term lossin the VICI index but this is quickly made bac k from sellingvolatility at the new higher levels of implied volatility.
Selling Credit Volatility P&L from selling short dated iTraxxM ain vol since 2006
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Crossover, Senior Financials and CD X IG.
Source: J.P . Morgan
Further information on theP&L from selling creditvolatility and the VICI indices
is available in:Credit Volatility Indices:Adding Alpha With CreditVolatilityD. White, March 2011
PnL of Selling Implied Vol (Sell Straddles, Delta-hedged)
No Exam
iTraxx Main iTraxx Main vs. Crossover
15%
20%
25%
30%
35%
40%Crossover 1m
Main 1m
4%
6%
8%
10%
12%
14% Main 1m
Main 3mMain 6m
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-5%
0%
5%
10%
Mar-07 Mar-08 Mar-09 Mar-10 Mar-11-4%
-2%
0%
2%
Mar-07 Mar-08 Mar-09 Mar-10 Mar-11
Greeks
Date:
6-Apr-10
Expiry:
16-Jun-10
Index:
Crossover 5y
No Exam
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Delta: Index position which generates a similar spread exposure than the option (in MtM terms) for small spreadmovements.
Gamma: As spreads move, the delta of an option changes. As a consequence, an initially delta-hedged option willnot be perfectly delta-hedged as spreads move. Gamma indicates the change in an options delta as spreadsmove.
Theta: If you buy an option, how much do you lose (in cents) in one day if everything else (spreads, volatility,rates, defaults) remains constant.
Vega: If you buy an option, how much do you make (in cents) if volatility increases 1% if everything else (spreads,time, rates, defaults) remains constant.
Source: J.P. Morgan.
Volatility Term Structure
Same strike, differentexpiry: Different
Volatility
No Exam
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Why?
Source: J.P. Morgan.
No Exam
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Volatility Skew
Same expiry, differentstrikes: different
volatility
No Exam
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Why?
Source: J.P. Morgan.
Disclaimer
JPMorgan is the marketing name used on research issued by J.P. Morgan Securities Inc. and/or its affiliates worldwide. J.P. Morgan Securities Inc. (JPMSI) is a
member of NYSE, NASD and SIPC. This presentation has been prepared exclusively for the use of attendees at Imperial College Structured Credit and Equity
Products" Course and is for information purposes only. Additional information available upon request. Information has been obtained from sources believed to
be reliable but JPMorgan Chase & Co. or its affiliates and/or subsidiaries (collectively JPMorgan) does not warrant its completeness or accuracy. Opinions and
estimates constitute our judgment as of the date of this material and are subject to change without notice. Past performance is not indicative of future
results. This material is not intended as an offer or solicitation for the purchase or sale of any financial instrument. Securities, financial instruments or
strategies mentioned herein may not be suitable for all investors. The opinions and recommendations herein do not take into account individual client
circumstances, objectives, or needs and are not intended as recommendations of particular securities, financial instruments or strategies to particular clients.
The recipient of this report must make its own independent decisions regarding any securities or financial instruments mentioned herein. JPMorgan may act asmarket maker or trade on a principal basis, or have undertaken or may undertake an own account transaction in the financial instruments or related
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hold a position in any securities or financial instruments mentioned herein.
Copyright 2012 JPMorgan Chase & Co.All rights reserved.
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