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Hedging Counterparty CVA with Credit Default Swaps

Article Quant Q&A · Author: a-rod
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Summary

The document explains how a firm can hedge counterparty credit risk embedded in a derivative portfolio and how CVA relates to the hedge. In a simplified example with zero recovery, a nonnegative derivative value is paired with a credit default swap on the counterparty. The CDS notional is set to the current derivative value, with continuous rebalancing, so the credit protection offsets exposure to counterparty default.

A second explanation emphasizes recovery assumptions: CVA depends on what can be recovered after default, and misestimating that amount can lead to a different valuation from the market. If a firm believes recovery will be higher than the market implies, it may sell CDS protection. These examples illustrate hedging and relative-value positioning, not guaranteed profit. The first setup assumes zero recovery and continuous rebalancing, while the document does not discuss transaction costs or broader implementation risks.

Key ideas

  • A CDS on a counterparty can hedge default exposure from a derivative with positive value.
  • In the simplified zero-recovery example, CDS notional tracks the derivative’s current value.
  • The hedge requires continuous rebalancing in the example presented.
  • Recovery assumptions affect CVA estimates and can create differing views of CDS value.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# How does one make money from CVA (Credit Valuation Adjustment)?


# How does one make money from CVA (Credit Valuation Adjustment)?












I am new to Quantitative Finance but have been doing a lot of reading on Counterparty Credit Risk.

I understand the definition of CVA being:

> "the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default."

I understand the Positive and Negative Credit Exposure due to defaulting Counterparties. I mostly understand the CVA Formula being:

$CVA =\int_{0}^{T} \! EE * (t) dPD(0,t)\,\mathrm{d}t.$

My question is, How does one (a firm, a bank...) make money from CVA trades? If all CVA is, is the expected loss of a counterparty defaulting, how is that possible to make money on these trades?

Can someone provide a basic vanilla example of how this is possible. Thanks!

## Answer by Daneel Olivaw (score 4, accepted)

https://quant.stackexchange.com/a/44471

Assuming zero recovery, let $\mathcal{C}$ be a counterparty you are facing on a derivative deal with value $V(t)$ and maturity $T$ such that $V(t)\geq 0$, for example an option. Let $CDS_\mathcal{C}(t,T)$ be the value at $t$ of a unit-notional CDS on $\mathcal{C}$ with maturity $T$. Then with the portfolio $\pi(t)=V(t)CDS_\mathcal{C}(t,T)$, namely a CDS trade with notional $V(t)$ (thus you need continuous rebalancing), you can hedge your risk of counterparty default and monetize CVA.

## Answer by vrume21 (score 1)

https://quant.stackexchange.com/a/44489

You’re missing an important term in your expression for CVA, the recoverability of assets in the case of default. Since this value can be difficult to estimate, it’s possible to incorrectly compute CVA. In the case where you know recoverability to be higher than what the market thinks it is, you might become a seller of credit default swaps.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.