# Credit Valuation adjustment (CVA) Hedges

I need to understand once CVA Desk has CVA number(Bilateral or Unilateral) for a Counterparty, how does it take hedge position.

for Eg: if CVA charge for my bank to JPM is 100K Dollars. What does that imply and how can CVA Trader use this number to hedge CVA risk of \$100K to JPM.

Please include any variable if I have missed.

Thanks

• A CDS comes to mind.
– Olaf
Commented Feb 24, 2016 at 9:57
• Can you please explain how and what amount of CDS should be used here Commented Feb 24, 2016 at 10:03

CVA is a price. Just like any price, you compute its sensitivities (greeks) and then use financial products to bring them as close to zero as possible.

It's not possible to derive a hedging strategy just by looking at the CVA figure, it's like asking what the hedging strategy of a product is if its price is USD 1M... You need the CVA greeks.

The particularity of CVA is that you always have a credit component (cf. https://en.wikipedia.org/wiki/Credit_valuation_adjustment) and this one can be hedged using CDS as Olaf said.

To continue from uness' answer (edit: just seen the OP was very old, but will leave here anyway!) . The greeks will be every element of market risk to which the the CVA is sensitive. Writing in words for celerity:

A CVA is a credit linked option on the underlying instrument. You are sensitive to the credit default- (specifically the swap obligation payment failure)- contingent +ve mark to market of the instrument, hence it is a credit linked option.

Consider the CVA on a receiver swap (receive fixed versus float). you are sensitive to:

• interest rates (rates delta)
• credit default intensity (credit delta)
• interest rate vol (due to optional asymmetric exposure profile)
• credit vol (modelled using stochastic intensity)
• credit - interest rate correlation (if rates are low with credit intensity high your CVA increases naturally, so you are short this correlation on this position, and in this case short credit and interest rate vol).
• there is also potentially material credit / rates gamma. You would probably be short credit gamma (the wider the intensity, the more the risk is priced in), much as you would in selling a CDS, depending on potency of correlation.

So - the deltas can be hedged with linear instruments, credit vegas will also be partially hedged with CDS (buying a CDS is short credit gamma), rates vegas are hedgeable. Credit-rates correlation, well, you probably just wear that.

Just a quick verbal overview, but hope that helps.

• Strictly speaking, CVA is not an option, not even a derivative, but its is approximated in practice by that of a derivative known as "Contingent CDS" Commented May 27 at 21:45

This presentation from Citi might help a bit regarding CVA hedging. If you scroll through you will find some examples which show their hedge structures (sic. suggestions).

https://www.boj.or.jp/announcements/release_2010/data/fsc1006a5.pdf

Me