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qiuxinhong
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Joined: August 25th, 2005, 11:14 pm

First to default CDS

November 9th, 2006, 7:08 pm

Can someone tell me how to hedge FTD CDS?
 
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jamesnowak
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Joined: October 23rd, 2005, 4:37 pm

First to default CDS

November 9th, 2006, 8:14 pm

Straight from Lehman Brothers guideThe issuers of default baskets need tohedge their risks. Spread risk is hedged byselling protection dynamically in the CDSmarket on all of the credits in the defaultbasket. Determining how much to sell,known as the delta, requires a pricing modelto calculate the sensitivity of the basketvalue to changes in the spread curve of theunderlying credit.Although this delta hedging should immunisethe dealer’s portfolio against smallchanges in spreads, it is not guaranteed to bea full hedge against a sudden default. Forinstance, a dealer hedging an FTD basketwhere a credit defaults with a recovery rate ofR would receive a payment of (1-R)F from theprotection seller, and will pay D(1-R)F on thehedged protection, where F is the basket facevalue and D is the delta in terms of percentageof face value. The net payment to theprotection buyer is therefore (1-D)(1-R)F.There will also probably be a loss on theother CDS hedges. The expected spreadwidening on default on the other credits inthe basket due to their positive correlationwith the defaulted asset will result in a losswhen they are unwound. The greater unwindlosses for baskets with higher correlationswill be factored into the basket spread.One way for a default basket dealer toreduce his correlation risk is by selling protectionon the same or similar default baskets.However this is difficult as it is usuallydifficult to find protection buyers who selectthe exact same basket as an investor.The alternative hedging approach is for thedealer to buy protection using default basketson other orders of protection. This isbased on the observation that a dealer whois long first, second, third up to Mth orderprotection on an M-credit basket has almostno correlation risk, since this position isalmost economically equivalent to buyingfull face value protection using CDS on all Mcredits in the basket.Figure 7 shows an example basket withthe delta and spread for each of the fivecredits. Note that the deltas are all verysimilar. This reflects the fact that all of theassets have a similar spread. Differencesare mainly due to our different correlationassumptions.Hedgers of long protection FTD basketsare also long gamma. This means that as thespread of an asset widens, the delta willincrease and so the hedger will be sellingprotection at a wider spread. If the spreadtightens, then the delta will fall and thehedger will be buying back hedges at atighter level. So spread volatility can be beneficial.This effect helps to offset the negativecarry associated with hedged FTDbaskets. This is clear in the previous examplewhere the income from the hedges is211bp, lower than the 246bp paid to the FTDbasket investor.Different rating agencies have developedtheir own model-based approaches for therating of default baskets
 
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CDOCubic
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Joined: March 3rd, 2007, 6:21 am

First to default CDS

March 16th, 2007, 1:17 am

D: =hedge ration=Delta of Individual CD/Delta of FTD