In this recent Paper Piterbarg we see everywhere (for example formula 7 there) dicounting collateral with the riskless rate. In the paper this is the case if the collateral corresponds exactly the value of the derivative.I think this is not the true cost of posting collateral. Assuming a bank is a massive margin/collateral lender. Then it has to fund the collateral used to secure its derivative. This means the cost of the collateral is the banks funding cost. How can this be the overnight rate? This would only be true if either the bank can use collateral received to make the posts for the negativ value derivatives. Or the bank has assets it can use to post for the collateral. But even in this case the cost of the collateral would be a repo rate. So did i miss something here?

Most institutions will only accept high-quality assets (such as T-bills) or cash for collateral, so the issuance-risk for the collateral itself is negligible for the amount of time the institution is funding itself (i.e. overnight).Also- because the institution is only borrowing overnight, the probability that it will default tomorrow is negligible-to-zero. So in this sense the "overnight rate" is a risk free rate.Does this answer your question?

I think that what you're touching upon ("the cost of funding") is FVA, but this charge only applies to the portion of a portfolio that is <i>not collateralized</i>.

Hi PvalAnal85,thanks for your response.I think of the following situation. An Institution is net behind and posting collateral for a longer time. Then they have to fund this collateral. Then the cost of posting collateral is the institutions funding cost. Not eonia. The simply earn eonia on the collateral from the counterpart. But they had to fund it. so there are funding cost.I could give an example: You buy a bond (assuming it is not so liquid) in an asset swap. Assume the bond is priced well over par. Then the asset swap is negativ on inception. The total pul calculated without considering csa costs would just be the buy of the packet at par (par asset swap assumed). But for the institution there is an immediate cashflow to post as collateral for the asset swap. From a total perspective this is fine The bank buys an asset (the bond) that is worth above par but only payed par. It has to compensate on the asset swap. But if you consider collateral to be financed overnight then it wont enter in the calculation as it also earns overnight. But in fact you payed the price in cash as you funded par to buy the asset swap package. And you post the bonds excess price over par as collateral immediatly. Meaning in all you had to fund the full dirty bond price. This is what the institution has to do. So it has collateral costs on the dirty price. And not on the clean price (which would be the result if you assume collateral is funded at eonia).

Hi,sorry i had some misspelling in the end. I meant the institution has funding costs on the dirty bond price. And not only on the par value (implied indireclty it collateral is just discounted with eonia rate)

Here is a related thread.

QuoteOriginally posted by: pcaspersHere is a related thread.Hi Thanks,i understand your argument there. But i think you consider the case of a perfectly hedged position. You are short a zero bond. And at the same time you receive C(0) which you could use to buy an equivalent zero bond. So in fact you are margin hedged so to speek. I wanted to ask more general how i could motivate margin hedging (in the sense displayed in pauls books on quantitative finance) by introducing collateral costs higher then the risk free rate into derivative pricing.As Paul deliberatly stated OTC Deals are never a hedge from a margin perspective to collateralized deals. Of course you can argue about CVA. I wanted to have a more direct argument of costs setting up a collaterlized account contrasted with the naked OTC Deal that is not collateralized. So i have chosen to look at cases where an institution definitly has funding costs out of collateral postings. And where there is (in the asset swap example) no instrument on the other side of the hedge that matches a negativ margin call on the derivative with some cash for the institution. Just discounting collateral with EONIA would suggest in the asset swap example the institution only has to fund the purchase of the par asw package. While in fact it has to put up the dirty price. And it is very likely it has to leave the collateral for quite a while on the counterparties account. Think af a par asset swap on inflation for example with a big balloon payment at the end. Just like your Zero Bond Cashflow. But in this case you dont have a liquid C(0) to set up a margin hedge (a collateralized derivative with exactly the opposite cashflows). Thank you nevertheless