imO discounting is all about hedging: [1] For negative future CFs you should ask yourself: What is the least amount of money that I need to invest today to receive 1$ in T (without taking on any credit risk!) [2] For positive future CFs you should ask yourself: What is the highest amount I can borrow with a promise to pay back 1$ in TFor [2] it is obviously the funding rate and actually for [1] as well, because - From the view of the trader the treasury desk is risk free (if the bank goes bankrupt it does not matter anyway) - The trader will not a find a different (almost) risk-free source that pays him a higher rate as treasuryHere I obviously assume that treasury offers the trader zero-bond investments for whatever horizon he asks for ...So why use OIS for collateralized trades then. Actually a collateralized trade is a portfolio of the payoff specified by the trade and the stochastic flows from the collateral account. Both parts of the portfolio should be discounted with the funding rate, which results in quiet a nasty valuation formula. Luckily for us, it turns out the this valuation formula is exactly the same as discounting the payoff specified by the trade on the OIS curve (i.e. OIS discounting is just a theoretical shortcut). However, the premise is of course that you can invest on the OIS curve, i.e. bootstrapping zero-bonds form the tradeable ois swaps. I have asked myself this questions a few times before but never had the time to really work it out. Does anybody have a solution to this?I want to add one last thing: OIS is NOT the correct discount rate because it is risk-free but simply because it is the typical rate specified in the CSAs (OIS is probably the closest thing you will find to risk free but this simply does not matter here). If the CSAs would use some Greek bond rate to determine the yield on the collateral account then this would be the correct discount rate.Would be happy to discuss .Cheers,Bernd

OIS rate can be used for example for MtM adjustment. For real world applications when a given sum is added as collateral it makes sense to use Federal Fund rate which is specified each morning for the previous day. On the other hand if one is trying to calculate effect of collateralization it makes sense to use OIS which somehow represent estimate of the risk free interest rate over the specified period of time. The difference between one-day cumulative FedFund rate and OIS rate over given period defines market risk.

Sry but I don't really get your point. The FedFundRate is usually part of the OIS curve ...

The difference between OIS and Fed Fund rates is similar to a risk free discount T-bond rate and correspondent risk free swap rate in which floating rate is risk the free discount bond rate.

Again: The FedFundRate is usually part of the OIS curve!What is the difference between the 1d FedFundRate and the 1d OIS rate supposed to be? It's 0 ...

What is the difference between the 1d FedFundRate and the 1d OIS rate supposed to be? It's 0 /// Here you are absolutely right. On the other hand if one talks about other period can we still state that for examplethe difference between the 1y FedFundRate and the 1y OIS rate is 0?

QuoteOriginally posted by: list1What is the difference between the 1d FedFundRate and the 1d OIS rate supposed to be? It's 0 /// Here you are absolutely right. On the other hand if one talks about other period can we still state that for examplethe difference between the 1y FedFundRate and the 1y OIS rate is 0?that's a good point

QuoteOriginally posted by: BerndSchmitzI want to add one last thing: OIS is NOT the correct discount rate because it is risk-free but simply because it is the typical rate specified in the CSAs (OIS is probably the closest thing you will find to risk free but this simply does not matter here). If the CSAs would use some Greek bond rate to determine the yield on the collateral account then this would be the correct discount rate.yes, exactly; if you replicate a collateralized payoff using a funding account, the colltateral account and the underlying, you get initial costs equal to the OIS discounted value of the payoff (it's easy and instructive to do this with some simple payoffs in a tree). What is important is that you have a symmetric funding account (same rate for borrow and lend) to do this, so the OIS disconuted value will never incorporate individual funding costs.

QuoteOriginally posted by: list1What is the difference between the 1d FedFundRate and the 1d OIS rate supposed to be? It's 0 /// Here you are absolutely right. On the other hand if one talks about other period can we still state that for examplethe difference between the 1y FedFundRate and the 1y OIS rate is 0?He's baaaaaaaack!!!!!

QuoteWhat is the difference between the 1d FedFundRate and the 1d OIS rate supposed to be? It's 0 /// Here you are absolutely right. On the other hand if one talks about other period can we still state that for exampleSry, I wasn't aware that there is a FedFundRate for > 1d (I'm not US based). As far as I'm ware of the FedFundRate is an uncollateralized rate?? Then it's obvious why this rate must deviate from the (collateralized) OIS curve for longer maturities.Nevertheless I'm still sure that you have to discount on the OIS and not the FedFund curve. Consider a collateralized payment in 1Y. This will accrue with the weighted 1d FedFundFixings over the next year (and not with the 1y FedFundRate). It's intuitive that you can only expect to get estimates of the future FedFundFixings from a product that is actually referencimg these fixings.The only open issue to me whether it is possible to replicate OIS zero-bonds from the OIS curve (built with swaps). Does anybody have insights on this?

QuoteOriginally posted by: BerndSchmitzQuoteWhat is the difference between the 1d FedFundRate and the 1d OIS rate supposed to be? It's 0 /// Here you are absolutely right. On the other hand if one talks about other period can we still state that for exampleSry, I wasn't aware that there is a FedFundRate for > 1d (I'm not US based). As far as I'm ware of the FedFundRate is an uncollateralized rate?? Then it's obvious why this rate must deviate from the (collateralized) OIS curve for longer maturities.Nevertheless I'm still sure that you have to discount on the OIS and not the FedFund curve. Consider a collateralized payment in 1Y. This will accrue with the weighted 1d FedFundFixings over the next year (and not with the 1y FedFundRate). It's intuitive that you can only expect to get estimates of the future FedFundFixings from a product that is actually referencimg these fixings.The only open issue to me whether it is possible to replicate OIS zero-bonds from the OIS curve (built with swaps). Does anybody have insights on this?Umm -- just because list says something, it doesn't make it true. This statement does of course hold for everybody (I guess myself included), but is especially relevant in the case of list. The effective fed funds rate is an unsecured overnight interbank rate, calculated by averaging the rate charged in actual transactions from the broker market. There are no other maturities on the menu.

bearish, of course I do not know all details which one can observed in the market trading. I know that FedFund rate is defined in the morning and covers previous day. And therefore it can be used in a similar situation something like MtM adjustment in collateral business. I do not know how FF rate is calculated to use it OIS for 1w or 3m. Then to see why swap rate does not discount rate one can consider the difference between zero coupon T-bond rate and swap rate on this bond rate. If T-bond rate promises $1 say in 3 months. Swap rate for 3 months does not equal to T-bond rate and also does not promises $1 in 3 months. If T- bond rate is a constant then swap rate is equal to this constant. Therefore the variability of bond rate is probably the primary reason why rates are different. If we assume that T-bond rate is a constant in all dates of exchange and only in one date T-bond rate is goes up or down we can calculate the effect of such variations. Then one can assume that similar deviations can occur at each moment during lifetime of the swap. Such deviations plus some systematic factors can effect on swap rate

QuoteOriginally posted by: list1bearish, of course I do not know all details which one can observed in the market trading. I know that FedFund rate is defined in the morning and covers previous day. And therefore it can be used in a similar situation something like MtM adjustment in collateral business. I do not know how FF rate is calculated to use it OIS for 1w or 3m. Then to see why swap rate does not discount rate one can consider the difference between zero coupon T-bond rate and swap rate on this bond rate. If T-bond rate promises $1 say in 3 months. Swap rate for 3 months does not equal to T-bond rate and also does not promises $1 in 3 months. If T- bond rate is a constant then swap rate is equal to this constant. Therefore the variability of bond rate is probably the primary reason why rates are different. If we assume that T-bond rate is a constant in all dates of exchange and only in one date T-bond rate is goes up or down we can calculate the effect of such variations. Then one can assume that similar deviations can occur at each moment during lifetime of the swap. Such deviations plus some systematic factors can effect on swap rateseveral good points.

You have to stop this, dave... You will doom us to an eternity of list's commentary.

QuoteOriginally posted by: MartinghoulYou have to stop this, dave... You will doom us to an eternity of list's commentary.I am trying a new approach. all others based on reason and fact have failed.