QuoteOriginally posted by: listQuoteOriginally posted by: ancastThere is no such discounting as an OIS discounting. It just derives from a mathematical fact in the derivation of the PDE when you establish a replicating strategy: "OIS discounting" is a shortcut to the more correct statement "risk-free discounting + adjustment due to the CSA collateral (assumed it is OIS remunerated ) clashes with the OIS disocunting". Besides a big assumption behind that is that the bank pays OIS on the collateral it receives and pays OIS to fund the collateral it needs to post. See here for a deeper analysis. For interest rates it is trikier, since in my opinion now swaps and FRAs are primary, not derivative secuirties. In the paper above also this issue is discussed.ancast, could you please to help with simple example to understand collateralization. In your paper, the 1-step binomial scheme let consider call option collaterized pricing. We have t = 0 and t = 1 = T; S ( 0 ) = S , S ( 1 ) is either Sd or Su ; call value C = C ( 0 ) Cd and Cu. From formulas (1) and(2) it looks that collateral is posted at t = 0 but its value 'V' does not specified in this case?List, I think that there is a bit of misunderstading when you read the paper.C is not the value of the call, but it is the collateral posted at time 0. The value of the derivative is V (possibly a call option if you wish). So, assuming a given fraction \gamma of the value of the contract is collateralized, you can write that C = \gamma V.The example I present in the paper is with 3 steps, but is ideally the same as in the one-step case.On a more general note, something important often overlooked when people refers to OIS discounting, is that it is implicitly assumed that parties agree to revaluate the contract, and hence post collateral, by using not a risk-free value, but the value that includes the effect of the collateral (the LVA in my paper). Now, since in practice collateral is remunerated with OIS, which is also what is generally considered the risk-free rate, it happens that the LVA is nil and OIS discounting is equivalent to risk-free discounting. More generally, if the collateral is remunerated at a different rate, then the LVA is not zero, and in this case there may be some divergence on how to revaluate the deal (e.g.: one party may affirm that the collateral has to be computed on the risk-free value of the contract, not the value obtained with OIS discounting), and the amount of collateral to post. This also shows that OIS discounting is just a shortcut working only under specific assumptions.