Skip to content
All library documents

Choosing Discount Curves for XVA and Uncollateralized Trades

Article Quant Q&A · Author: abhinav mehta
Read the original

Summary

The document explains why LIBOR is not automatically the right discounting basis for valuing uncollateralized derivative exposure. LIBOR may have served as a legacy proxy for a bank’s unsecured funding cost, but an institution-specific funding spread can differ from LIBOR and can instead be expressed relative to a collateralized curve. The choice affects which basis risk must be hedged.

The answers recommend valuing derivatives first using the curve specified by the collateral agreement, then measuring adjustments such as CVA and FVA from that common base to reduce double counting and improve comparability. A separate answer distinguishes CVA, which reflects counterparty credit risk, from ColVA, which relates to collateral terms and remuneration. The discussion is conceptual and provides no calibration data or universal curve prescription; appropriate treatment depends on the trade’s collateral and balance-sheet assumptions.

Key ideas

  • LIBOR is not necessarily a reliable proxy for an institution’s uncollateralized funding cost.
  • Expressing a funding spread against LIBOR or a CSA curve changes the basis exposure that may need hedging.
  • A CSA curve can provide a consistent starting valuation before adding XVA adjustments.
  • CVA and ColVA represent distinct effects, tied respectively to counterparty risk and collateral terms.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# Discounting for XVA


# Discounting for XVA












I was thinking that since XVA is on uncollaterized exposure, we should be using LIBOR discounting environment. Why don't we do that?

## Answer by Attack68 (score 3)

https://quant.stackexchange.com/a/51191

Libor, besides its name, is not a good proxy for uncollateralised funding. In fact, a large bank I worked for had an uncollateralised funding curve which was a a spread of +100bps to Libor.

The fact that it was a spread to Libor was for legacy reasons and easier to adopt to existing systems. However, a spread of say +115bps to CSA was equally appropriate.

When you trade a collateralised (CSA) versus uncollateralised trade and want to hedge there is an element of how you account for the trades on balance sheet.

If you mark as a (generally fixed) uncollateralised spread to Libor then you will also need to hedge the LIBOR/CSA basis. If you mark as a (generally fixed) uncollateralised spread to CSA then you can effectively ignore the LIBOR part of discounting completely.

A second point is that to provide an effective comparative base every derivative should be first valued with the CSA curve and then the adjustments (CVA/FVA/KVA) measured from that basis, this avoids any kind of double counting, and provides a standardised means of comparison.

## Answer by Jose Pedro Melo (score 0)

https://quant.stackexchange.com/a/51198

Changing the discounting curve is not related to CVA, but to ColVA. CVA stands for the counterparty risk in uncolletarized trades, but the discounting is related to the CSA terms of collateral remuneration and risk free rate.

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.