Collateral, OIS Discounting, and Cash Flows in Interest Rate Swaps
Summary
The discussion explains what collateralization means for an interest rate swap and why standard collateral agreements are associated with OIS discounting. When a swap is a liability to one counterparty, that party posts collateral to the counterparty holding the asset, reducing exposure to default. Cash remunerated at the OIS rate is described as a common collateral form, though other assets may be accepted under a credit support annex.
The answer illustrates the mechanics with a receive-fixed swap example: after a cash flow, the swap is described as an asset to one party, and collateral is posted in that amount. The recipient then pays interest on the collateral at OIS. This illustrates collateral and discounting concepts, but it does not work through the requested multi-curve valuation or calculate a full schedule of swap cash flows. The numeric example also uses a notional different from the question’s stated notional, so it should be read as an illustration rather than a worked valuation of that specific contract.
Key ideas
- Collateral protects a swap counterparty against default by the party that owes value.
- Cash collateral remunerated at OIS is described as a common standard arrangement.
- The collateral terms help explain the use of OIS discounting for standard swaps.
- Collateral earns interest, which is paid according to the agreed remuneration rate.
- The example does not provide a complete multi-curve valuation of the stated swap.
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Full text
# Collateralized Interest Rate Swap # Collateralized Interest Rate Swap I am struggeling with the wording "Collateralized" IRS and try to get an understanding out of it based on an example. Especially what it means that in the multi curve models the expectations are calibrated such that the net present value of a swap equals zero (PV Fixed - PV Floating). I have the following IRS: ``` Notional 1 Mio. Euro Fixed Rate Leg = 2% Floating Rate Leg (Tenor) = 6M Euribor without spread Maturity = 2 years Tenor Floating = 6 Month Tenor Fixed = 12 Month Day Count Conventions Fixed = Actual/360 Day Count Conventions Floating = Actual/360 Discount Curve = OIS USD ``` How would an example look like (with math and with numerical numbers)? ## Answer by Attack68 (score 4, accepted) https://quant.stackexchange.com/a/36108 Collateralised means that when the IRS is negatively valued (i.e. a liability) for one of the counterparties then they post collateral to the other respective counterparty (i.e. the asset holder) to protect them against default of the liability owner. Collateral comes in many forms. The 'gold standard' is cash remunerated at the OIS rate, but it could be corporate bonds or equities or some other weaker form of collateral. For standard swaps cash@OIS is the default collateral type specified in the CSA (credit support annex) and this is why the discount factor curve used for standard IRS is the the OIS curve. Your (annual) fixed leg is 2%. Suppose you received fixed on EUR100mm and the 6M IBOR rate was 1%, this would imply you make a payment of EUR0.5mm in 6M time. At that point the remaining cashflows on your swap mean it is now an asset of EUR0.5mm, so the counterparty will repay the cashflow, that you just paid to them, back to you. But now the money is in the form of collateral and you will pay the counterparty interest at OIS on the EUR0.5mm.
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