Discount curve and payment frequency

Question

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 1

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.