Why Payment Frequency Does Not Set the Discount Curve Tenor

Summary

The document addresses whether the tenor of a LIBOR rate used for discounting should match a swap leg’s payment frequency. Its answer says that LIBOR is generally not the preferred discount curve for uncollateralized trades. Because LIBOR includes a credit spread above a risk-free rate, discounting with LIBOR can incorporate counterparty credit effects into valuation while credit valuation adjustment (CVA) separately accounts for that risk, potentially counting it twice.

Instead, the response recommends using an overnight indexed swap (OIS) curve for discounting and applying explicit xVA adjustments. It also notes that LIBOR-based discounting would only be a plausible reflection of credit risk if the counterparty’s credit risk resembled that of LIBOR panel banks, a condition the answer considers unlikely for uncollateralized trades under the regulatory environment it describes. The response therefore redirects the question away from choosing a LIBOR tenor based on monthly, quarterly, or infrequent payments. It offers a concise general recommendation, not a detailed treatment of all market conventions, curve construction choices, or the specific xVA components relevant to a particular trade.

Key ideas

• The payment interval alone does not determine an appropriate discount curve tenor.
• LIBOR includes a credit spread, so using it for discounting can embed credit risk in valuation.
• Combining LIBOR discounting with CVA may count counterparty credit risk twice.
• The answer recommends OIS discounting with explicit xVA adjustments for uncollateralized trades.

Tags

# Discount curve and payment frequency


# Discount curve and payment frequency












In case of uncollateralised trades, where we use LIBOR rates for discounting, does the LIBOR tenor have to match with the payment frequency?

For example, one of the swap leg pays USD floating amount every 3 months, does this suggest that we should use 3M USD Libor for discounting? (and 1M USD LIBOR for monthly payment etc.)

If this is true, what if the payment frequency is once every 3 years. What would be the best LIBOR tenor to use for discounting?

If not, is there any market convention of choosing the suitable default LIBOR curve for different currencies, irrespective of the payment frequency?

Thanks.

## Answer by Adam N. (score 6)

https://quant.stackexchange.com/a/36332

Better yet, don't use LIBOR for discounting at all.

Since LIBOR involves credit spread over the risk free rate, using LIBOR for discounting would adjust the deal's market value to reflect some amount of credit risk. Hull and White argue it's not generally the best idea, since it would mean double-counting, as one also normally computes the CVA to handle this risk. Also, it'd be admissible only if the counterparty's credit risk was comparable to LIBOR panelists, ie. if it was a bank, but having an uncollateralized deal with a bank is unlikely in the current regulatory environment.

If you want to value uncollateralized trades, you're better off using OIS as the discount curve, with explicit xVA adjustments.

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