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BLOBY
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First To Default of EDS

July 8th, 2004, 1:09 pm

Hi, does somebody got an idea of how it would be possible to price a First To Default on 5 Equity Default Swaps ??I guess it's not the same calculation of trigger probability as CDOs, because EDS are OTM puts....Any suggestions ?
 
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eiriamjh
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First To Default of EDS

July 8th, 2004, 1:32 pm

Monte-Carlo, perhaps?e.
 
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BLOBY
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First To Default of EDS

July 8th, 2004, 2:10 pm

like an equity structured product indexed on a basket ...?
 
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Herbie
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First To Default of EDS

July 8th, 2004, 8:42 pm

BLOBY,here's my answer, based on gut feeling rather than tried / tested. EDS are often quoted similarly to CDS, i.e. term structure of spreads. This makes sense as EDS basically same as CDS, except the 'event' is defined differently, and as Pr(70% drop in equity) > Pr(default), EDS spreads are much higher than CDS spreads. Regardless of the exact definition of the event, the spreads allow you to work out the market's view of the probability of an 'event'. I.e. it doesn't matter whether it is a FTD on either EDS or CDS.Thus to price FTD on EDS, why not just use a standard FTD (of a basket of CDSs) model. The market standard is a Gaussian copula per David Li's approach. When you calibrate marginal default probabilities (usually done off CDS spreads), just use EDS spreads instead. Make sure to set the LGD assumption to whatever the EDS will pay post event.To get the 'right' correlation, you really need to have an observable market in tranched EDS products (cf as there is now an observable market on tranched CDS products like iBoxx). This market doesn't exist yet, so you can either use asset correlations (i.e. based off implied correlation credit market data, e.g. FTD broker quotes) or equity correlations.
 
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blob
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First To Default of EDS

July 8th, 2004, 10:01 pm

Thank you a lot Herbie for your answer, but I have 3 questions :1- what is "LGD assumption" ?2- is it really correct to say that we can infer trigger probability from EDS spread ? Because EDS spread is by definition the premium (running and not upfront) of an american binary put....3- how do you caculate asset return correlations ? I suppose it's with Merton model, but how do you calculate asset (and not equity) volatility ??Thank you in advance.
 
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Herbie
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First To Default of EDS

July 9th, 2004, 10:53 am

1) LGD is (in CDS language) 100% - recovery rate assumption. I..e what do you as the protection buyer receive when an event defaults? Usually assumed to be 60%. Or in EDS language, what is the size of the binary payment you receive when the equity first falls below 70% of the original value? I understand this is usually set at a fixed binary amount (50%?).2) EDS spread in market just means: what do I have to pay on a running basis to buy protection such that PV today = 0. This is used to calibrate hazard rate of a poisson process, and thus the probability of an event occuring at a time t.Let me turn your question around: do the mathematics of hazard rates / poisson distributions (and thus the maths of a CDS model) understand or care about the definition of an 'event' - i.e. whether an event is either a default, or a 70% drop in equity price?You can look at an EDS in 2 ways:(i) like a (binary) cds except the event is defined differently. Key parameter would be spread.(ii) like an equity option. Key parameter would be volatility.There should be a link between these two views, i.e. for a EDS market spread you should be able to back out an implied volatility and vice-versa.3) asset correlations are can be viewed as 'gaussian copula' correlations - see the Risk Metrics paper by D Li in1999. Thus if you want asset correlations use correlations that are relate to products where the market quotes are based on a gaussian copula model. in other words, use implied iBoxx / Trac-x or FTD broker quotes. People also say (via Merton) that equity correlations are a proxy to asset correlations, because the total value ofa firm is constant - changes in equity must be offset by changes in debt. Thus I don't think you would calculate asset volatilities (unobservable anyway) - you just basically say equity correlation (observable) = asset correlation. Some people pre-process equity correlations, though I don't have any details.In the absence of EDS implied correlation data, the most relevant correlations for EDS would be probably be equity correlations, although you'd need to factor in the skew, i.e. the fact that it is empirically seen that implied correlation is a function of tranche seniority. Can't see an obvious way to do this yet - the market hasn't evolved enough. It is likely that you will need to reserve against your guess of correlation.
Last edited by Herbie on July 8th, 2004, 10:00 pm, edited 1 time in total.
 
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BLOBY
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First To Default of EDS

July 9th, 2004, 12:13 pm

Thank you very much for these explanations ;Last question : would you say that EDS implied correlation should be equal to CDOs or FTD implied correlation ?Because equity correlation is often higher than default (or spreads) correlation.....
 
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Herbie
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First To Default of EDS

July 9th, 2004, 1:39 pm

I would agree - equity implied correlations I would expect to be higher than basket credit derivative implied correlations. Don't forget however that there is the skew effect to take into consideration.
 
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BLOBY
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First To Default of EDS

July 12th, 2004, 1:09 pm

thank you Herbie, but how would you take in account the skew effect ???
 
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Herbie
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First To Default of EDS

July 14th, 2004, 4:10 pm

Well there is no real answer, the markets aren't developed enought yet. You'll have to take proxies (e.g. CDS index tranches implied correlation smile, or smile of small NTD basket implied correlation for similar obligors to your EDS reference entities), or make guesses / approximations.
 
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Squal
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First To Default of EDS

October 8th, 2004, 6:52 am

Hi all,I would like to test my feeling about the calibration of an EDS curve (I junior in this field).Do you guess that to calibrate the EDS curve it is stupid to say that the premium leg should be equal to the value of on digital put option ?I guess that EDS are like an "installment put" (Option were you never pay the full premium)Thus the calibration equation is: Sum of discounted flow on risky curve = value of a digital put optionCould someone give me the feeling about that approach ?What is wrong in my derivation ?Regards,
 
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Squal
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Joined: January 21st, 2004, 9:14 am

First To Default of EDS

October 8th, 2004, 6:52 am

Hi all,I would like to test my feeling about the calibration of an EDS curve (I junior in this field).Do you guess that to calibrate the EDS curve it is stupid to say that the premium leg should be equal to the value of on digital put option ?I guess that EDS are like an "installment put" (Option were you never pay the full premium)Thus the calibration equation is: Sum of discounted flow on risky curve = value of a digital put optionCould someone give me the feeling about that approach ?What is wrong in my derivation ?Regards,