In the fixed income literature, is the CSA discounting the same as OIS discounting? Seems they're referring to the same thing, but couldn't find an explicit statement confirming it.
"CSA discounting" does not give you a lot of information: it just means the collateralisation of the trade follows the rules agreed upon between both parties in the Credit Support Annex. But you don't know what those rules are so you would not necessarily be discounting your transaction's cashflows at OIS. I have heard people use "CSA discounting" interchangeably with "OIS discounting" but it is because they assume a perfect CSA.
"OIS discounting" means that you are able to discount the cashflows of the transaction using OIS. Typically this means that your CSA is perfect, meaning both parties post cash (or cash-equivalent), daily, without thresholds or minimum transfer amount.
However, there is still the question of the currency; what does "OIS discounting" for a cross-currency swap mean? Are you posting cash in (and discounting your xccy at the OIS of) the currency of leg 1 or leg 2? Market-standard swaps have conventions for this but it is not necessarily clear.
CSAs can be highly customised with the following parameters:
- Instruments you can post (cash -> which ccy?, gov bond, corp bond, ... ?)
- Is it two-way or one-way? (both parties post or just one?)
- How often do you post? (daily, weekly, monthly, ...?)
- Threshold: from what level of Mark-To-Market (PV) do you start posting?
- Minimum Transfer Amount: what is the minimum MTM move which would require collateral to be transferred between parties?
- Independent Amount: one party can be asked to post an initial margin from day 1 on top of everything else
- Optionality: do parties have the option to choose what they want to post through time?
- Structured CSA: e.g. capped total amount posted has become quite popular in the last few years, but you could complicate it further if you wanted to
Custom CSAs are generally put in place to mitigate specific credit risks, including jump-to-default for example. They can also be found as legacy from a time when the pricing of all those parameters was believed to be negligible. All of those will impact your pricing through CVA, FVA, DVA, CTDVA and capital charges.
OIS discounting is a subset of CSA discounting... technically they are not the same thing. CSA actually stands for Credit Support Annex, which is an Annex to your ISDA agreement with your trading counterpart that governs how your derivative trade is collaterallized (or not). Without the CSA agreement, the trade will get priced at the highest level of counterparty risk and the CSA charge will be significant. Often if there is good GC-eligible asset to collateralize the trades (among major firms) then the discounting is off of OIS curve, hence "OIS discounting".
It depends on your CSA agreement.
If there is a clearing house inside the collateral process governed by your CSA, I might suppose that the CSA discounting will be OIS minus a fee.