Arvanitis and Gregory (2001, Credit: The Complete Guide to Pricing, Hedging and Risk Management) suggest a method to hedge the counterparty risk on an IRS by a CDS. In short this method consists of hedging the IRS' mark-to-market value by buying a CDS with a notional equal to this m-t-m. Obviously, the CDS notional needs to be rebalanced since the IRS' m-t-m is fluctuating as well. They furthermore state that "if the default curve widens, the P&L on the swap will be negative (since the risky PV will decrease), while the long CDS position will increase in PV. However, it is only by chance that these will cancel. The authors suggest to choose the CDS so as to delta hedge, i.e. the deltas of the IRS and CDS are equal (delta is defined here as change with respect to a 1 bp change in the default swap spread)". They suggest e.g. to change the maturity of the CDS in order to get the required matching delta.I don't understand this, because the IRS has a delta (basis point value) based on a higher notional, e.g. a 10Y IRS, €100m notional swap has a bpv of approx. € 81,000. Let's assume the m-t-m of this IRS is € 5m, so effectively one would start to hedge € 5m by a CDS, which has a bpv of approx. € 4,000. The IRS and CDS delta's are different, but how would you obtain equal delta's? Would you have to make an adjustment, e.g. (exposure/IRS notional)?Thanks in advance,Kim

Hey Kr0,CDS' bpv is its duration, therefore changing the CDS' maturity will get you the right delta... or am I not getting your pbl?

Hi Ri,I agree that increasing the CDS' tenor will increase its basis point value (bpv). However, on a 10Y tenor the bpv of a € 5m notional value CDS is much lower than a € 100m notional value IRS. The former is approx. € 4,000, and the latter € 81,000. Increasing the tenor of the CDS will not be sufficient to increase the bpv from € 4,000 to € 81,000. Besides that I believe most liquidity in the CDS market is around 3-5Y, so there's another limitation. However, I'm not sure whether bpv is the same as delta in this context. I think it's not, but I don't know what it should be.

Ok you got a €5m mtm for the IRS. Credit risk can either be variation of IRS mtm due to widening of credit curve OR instantaneous default.You cannot hedge both risks with one instrument. What I'm getting at is that if you're delta hedging credit curve variations, the CDS notional does not have to be equal to the IRS mtm or its notional, or whatever (you're therefore definitely not hedged against default risk).This means that in your example, the CDS notional doesn't have to be €5m....Still not 100% sure that this is what you want though?

The credit risk on an IRS transactions is losing the positive mark-to-market value in case the IRS counterparty defaults. In addition to a widening of the credit curve or instantaneous default, credit risk is also driven by a change in interest rates, which effectively determine the change in mark-to-market, hence the exposure. I understand your point that by changing the CDS notional, it is possible to create a CDS with a delta equal to the IRS delta. However, this implies a CDS notional, which is much higher than the mark-to-market of the IRS (which needs to be hedged against credit risk). I'm only interested in hedging the credit risk, e.g. in case of an instantaneous default this is the (positive) mark-to-market value of the IRS. As the m-t-m value of an IRS is constantly changing I would also have to adjust the notional of the CDS, which is used to hedge against the credit risk on the IRS. At inception of an IRS the m-t-m value is usually zero, so what would be the appropriate amount to be hedged? The IRS' expected or worst case exposure?

you can't set up a good static hedge here for the reasons you note, i.e. the cds provides a static amount of protection, wheras the irs requires an amount of protection that is a function of interest rates. Furthermore, a credit spread dv01 hedge <> an instantaneous default hedge (unless you have warning of default).You have two options: (i) dynamic cds hedge + good judgement, (ii) credit contingent interest rate swaps which the major houses now market. These products should be a good hedge of the credit risk of an IRS counterparty defaulting.

Hi KR0,As Herbie mentioned, credit contingent interest rate swaps is probably a good alternative for hedging both the price risk and default risk.If you are really looking to hedge the default risk (of the counterparty), and not so much concerned about the price risk, then you are probably better off by just hedging with CDSs..where the notional of the CDS is either equal to the IRS MTM, or is slightly higher than the IRS MTM (to provide a small cushion for the interest rate movement before the occurrence of a credit event on the counterparty). Hope it helps.Rgds

Thanks for this information. Do you also have information on credit contingent interest rate swaps? Google did not deliver a usuable result.

Let's assume the 5-years CDS market for a certain credit trades 35-40. I would like to hedge the credit exposure (i.e. positive mark-to-market) on a 5 year, € 100 million IRS transaction on this counterparty by using a CDS. Let's assume the counterparty is paying fixed and receiving floating under the IRS and the potential future exposure (i.e. worst-case exposure) given a 97.5% confidence level is € 3 million. This amount would normally have to be allocated as a credit line. However, in this case there's no credit line and I would like to use the CDS to hedge the credit exposure under the IRS.The idea is to buy a CDS with a notional equal to the potential future exposure, i.e. 3 million and embed the hedging costs (CDS premium) into the IRS transaction quote. Paying 40 bps (per annum) credit spread for 5 years protection on a € 3 million notional implies approximately € 54,000 present value (I ignore the fact that an upfront CDS premium is basically the PV of a series of future payments of 35 bps adjusted for the default probability). If I embed this value in the IRS this will roughly be 1.2 bps extra in the IRS (the basis point value of a 5Y, € 100m IRS is approx. € 45,000). Given the confidence level (97.5%) there's only a 2.5% chance that the IRS market value in the event of default will be more than € 3 million. Assume that I can (competitively speaking) embed this 1.2 bps in the IRS transaction, would I have to bother to rebalance the hedge at all? I wouldn't think so. Who can comment? Do you think I should hedge the potential future exposure?