Hedging CVA Requires Sensitivities, Not Just the CVA Amount
Summary
The document clarifies why a credit valuation adjustment amount alone does not determine a hedge. CVA is a price, so a desk first needs its sensitivities to relevant market factors; hedge positions are then selected to offset those exposures. The credit component is commonly addressed with credit default swaps, while other risks may call for instruments tied to rates or volatility.
For a receiver interest rate swap, the discussion lists sensitivities to interest rates, default intensity, interest rate volatility, credit volatility, and the correlation between rates and credit. It also notes possible nonlinear exposure, including credit and rates gamma. Linear instruments can hedge some delta exposures, and CDS may partly offset credit volatility exposure, while rates volatility can be hedged separately. Correlation risk may be difficult to hedge and may remain on the book. These are qualitative examples rather than a specific hedge recommendation: actual positions depend on the portfolio’s exposures, model assumptions, and available instruments.
Key ideas
- A CVA amount is a valuation and does not reveal the hedge without its risk sensitivities.
- CVA hedging starts by measuring sensitivities to the market factors that affect the adjustment.
- Credit default swaps can hedge the credit component and some credit volatility exposure.
- A receiver swap CVA may also carry rates, rates volatility, credit volatility, correlation, and nonlinear risks.
- Some risks, especially credit and rates correlation, may be difficult to hedge directly.
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# Credit Valuation adjustment (CVA) Hedges # 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 ## Answer by byouness (score 4) https://quant.stackexchange.com/a/32066 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. ## Answer by Mehness (score 4) https://quant.stackexchange.com/a/32070 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. ## Answer by user20172 (score 1) https://quant.stackexchange.com/a/32073 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
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