# CDS - Delta

Any ideas what are the inputs used to measure the delta of a CDS.

Are you talking about the delta when comparing a CDS tranche to its overall index?

By delta of the CDS, you probably mean delta wrt to the stock, yes? If so, you can use a Merton model set-up where you need the value of the debt, risk free rate, asset vol, and, uh, maybe that’s it.

I sort of know that delta is the underlying option divided by underlying spot price. For CDS, it is slightly a new green field for me

Are you trying to hedge the CDS with a stock? What are you trying to do exactly and we can probably hep you out better.

Thanks Joe, I am trying to calculate the underlying delta of a long CDS

Delta with respect to what?

I am guessing you mean delta in the sense of DV01. The DV01 for a simple CDS contract is the present value of the annuity stream (insurance premium i suppose is a decent way to look at it) using the swap curve as your discount rate and then multiplying each year’s present value by 1-cumulative probability of default. This is referred to as the “risky annuity”. In other words, DV01 is the change in dollar value for a 1bp change in spread as calculated by the risky annuity. DV01 keeps the swap rate unchanged, makes an assumption for recovery, and simply tests the dollar value change for a 1bp increases/decreases the spread or strike of the contract. This 1bp change in spread, when taken together with the assumption for recovery, can effectively be used to back out cumulative probabilities of default for each point along the duration of the contract. A 1bp increase/decrease, all things equal, will imply a higher/lower probability of default. This in turn will decrease/increase your DV01. As an aside, when dealing with tighter names, your assumption for recovery will matter much less than when you have a contract trading at a wider level. Thus, the higher the spread (keeping recovery and swaps rates unchanged), the lower the DV01. As a final thought, whether or not CDS is trading in points up front + 500bp running or as a standard floating single name, the calculation of this “risky annuity” is the same. I hope this helps.

agree w mib20 above if you’re looking for a \$ risk measure. looks like you’re looking for a % risk measure, which you’re calling CDS delta. delta ‘relative to what’ means what is the underlying risk factor that you’re measuring sensitivity to. the underyling for a stock option is the stock, so delta is relative to the stock % change. the underlying for a CDS is the bond (reference credit). a CDSwap is really a misnomer. the dang thing is a put option (for the party long CDS) on the credit, effectively. so if you’re looking for the CDS delta, you’re likely looking for the delta of the put option on the bond. which would imply, the delta is relative to the bond % change… …which in turn would depend on the swap curve and spread (specific to reference credit) above it. assuming a constant swap curve (note that the default event may be correlated to general level of rates, however), another definition of the delta you could use is the sensitivity to 1% change in spread for the reference credit. now we are talking of a ‘spread duration’ type risk measure. i.e. the bond put option’s spread duration. wow, strange beasts inhabit our field…you discover a new species everyday. btw, the DV01 approach mentioned by mib20 is a ‘dollar spread duration’ type risk measure. disclaimer - i’m not a credit specialist. others can correct me if they disagree. enjoy the safari…

I would say that the underlying for a CDS isn’t really a bond because: a) a CDS is about the credit of the company not a particular bond. In particular, all senior unsecured debt is usually deliverable b) CDS pays off based on probability of bankruptcy (and all those 7 problems that trigger credit events). That ought to be more clear in price movements of equity not debt. Anyway, agree that the underlying of a CDS is not directly a security so the term delta is just not clear unless there is some specific plan.

I guess this sounds nice in theory, but as Joey mentioned, a CDS contract is based on the reference entity and can have the ref entity and “downstream bonds” delivered into it. Because each bond has different coupons, convexity (negative in the case of some that are callable), and duration, each bond will have a different theoretical delta in the case here. I suppose you could make the case that the delta for CDS could be the 1% change in the Z-spread of an equal tenor bond, relative to the spread of the underlying CDS contract, but in reality this is not looked at all that much, since in theory they should be relatively the same (given that you can fund your bond at libor). In practice, we will use dollar duration (DV01) to hedge our p/l, but this leaves us either net short/long default exposure. If we are long default exposure, any jump to default will crush us. Think about it, a \$100mm net long exposure to a credit that goes bankrupt will leave us liable for \$60mm (assuming 40% recovery). Being duration matched along the curve will do nothing for us in this case.

uhohcfa Wrote: ------------------------------------------------------- > Are you talking about the delta when comparing a > CDS tranche to its overall index? i bet that is what he is referring to. That’s at least the way I know it.

I get the feeling mib20 should be allowed to put “mib20, CFA 2010” on his business cards…

the CFA curriculum barely even scratches the surface of credit derivatives unfortunately. they need to fix this issue. its actually quite astonishing that you can get a CFA with minimal knowledge of the credit side.

All: Thanks for the detail information. This has been very useful for me. DV01 is what I was looking.

chrismaths Wrote: ------------------------------------------------------- > I get the feeling mib20 should be allowed to put > “mib20, CFA 2010” on his business cards… We will see if I can call myself a June 2009 LII candidate on July 29th. Hope so. If I fail, ethics will be the reason why. Thought LI was actually relatively easy, but wouldnt be surprised if my ethics score was around 50-70%. I obviously work in this product (CDS), and was also quite frustrated with the lack of credit material covered in LI.

DV01 and Delta are different. DV01 = Dollar Value of a Basis Point Move, is essentially what mib20 described, using a BP move across the entire spread swap curve. While this a standard output measure, it’s typically does not happen during an event for names. Wamu for example is trading inverted CDS curve, with any BK news and I would bet the longer dated CDS would widen to near the same levels as the shorter dated, (ie the spread curve would flatten, but not completely). The DV01 assumes flat move across all dates. Delta on a CDS, the way I know it, refers to price movements on index tranches, such as the HY/ABX CDX and different levels of protection, given a move on the index. They are often quoted by the dealer. For instance you can buy the 5 yr 0-3% IG CDX9 tranche which has an estimated delta of 3.4 for 59 upfront points and 500+, and this delta changes due to gamma and levels on the index. I do not trade these but do receive quotes by dealers.

rohufish Wrote: ------------------------------------------------------- > the CFA curriculum barely even scratches the > surface of credit derivatives unfortunately. they > need to fix this issue. > > its actually quite astonishing that you can get a > CFA with minimal knowledge of the credit side. Not just credit derivatives - freaking credit. I think you could get a charter and not know the difference between a AAA bond and a B bond.

rohufish Wrote: ------------------------------------------------------- > the CFA curriculum barely even scratches the > surface of credit derivatives unfortunately. they > need to fix this issue. > > its actually quite astonishing that you can get a > CFA with minimal knowledge of the credit side. Not just credit derivatives - freaking credit. I think you could get a charter and not know the difference between a AAA bond and a B bond.