When valuing an Interest rate swap, counterparties will typically issue the contract at a Libor + credit premium, e.g. Libor +2%. When valuing a swap, we require a LIBOR forward curve and Discounting curve. Under the multi-curve methodology, we have an OIS discounting curve and the forward curve based on LIBOR rates.
1. how do you account for the credit spread e.g. 2% in the LIBOR +2%? Do you simply add it to the forward curve rates (which is based on libor flat), and also to the OIS discounting curve, or only add it to the forward curve and not the discounting curve?
Is the OIS discounting curve a daily compounded curve, i.e. there is a discounting factor for every day of the month in the curve (or are there different ways in which this curve can be represented in)?
Are there any market/publically available OIS discounting curves published somewhere (free)?
4. With regards to the Transition to SOFR, will the same OIS discounting curve that was used to value swaps under a LIBOR agreement be used to value a swap that is transitioning to SOFR, (since the curve is not directly determined from the floating leg (libor)), Or will a different OIS discounting curve be constructed for valuing SOFR swaps in the transition, where the OIS discounting curve will be constructed out of OIS SOFR swaps?
(I saw that an OIS curve can be constructed using LIBOR swaps or SOFR swaps for the long end of the OIS discounting curve).