Rationale for OIS discounting for collateralized derivatives?

Question

Can someone explain to me the rationale for why the market may be moving towards OIS discounting for fully collateralized derivatives?

Answer 1

Most counterparty agreements specify some sort of ois rate for the interest paid/received on posted collateral. So the OIS rate is the appropriate one to use for discounting future cash flows.

Prior to 2008 the OIS/Libor spread was small and stable, so you didn't really need to worry about this, but now it's much larger, so people are taking it into account. The reason it's "big news" now is that properly switching pricing systems over to use OIS discounting is a large change, so most places are only now getting this online.

Answer 2

The OIS rate is more stable than Libor, right? And according to this article from Risk Magazine:

The party that is owed money at the end of the swap will have been paying an OIS rate on the collateral it has been holding, and so the ultimate value of the cash it will receive will be the sum it is owed minus the overnight interest rate it has had to pay on this collateral.

Answer 3

If you assume that you do not have any market risk (a strange assumption, but it would hold for example if you are fully hedged), then a (correctly) collaterlized derivative does not have any net future cash flow. Clearly: if the derivative contract has a cash flow of -X, its value will go down by X and the collateral account will have a cash flow of +X (the corresponding collateral will be returned).

If there is no future cash flow, there is no discounting (in the sense of funding costs). However there is a new question now: what is the correct amount of collateral C we should post in t=0 to collaterlize the cash flow in t=T?

Since collateral is accrued according to the collateral contract by the OIS rate we would like to have that the accrued collateral account matches the cash-flow, that is

C * (1 + r * T) = X

where r is the OIS rate. That is we determine the collateral by OIS discounting

C = X / (1 + r * T).

OIS discounting is the way to determine the amount of collateral we have to post.

(You can make this argument mathematically correct (under some general assumptions) and show that collateralization is like having a different currency which has its own interest rate, I have some stuff on this (paper, spreadsheet for OIS bootstrapping, source code) here: http://www.finmath.net/spreadsheets/curvecalibration/ )