There are a number of papers that say if you have a collateralised LIBOR swap, you should use an OIS curve for discounting. This is based on no arbitrage arguments. Then there is the "Two Curves One Price" paper by Bianchetti. He uses no arbitrage arguments as well, but come to the conclusion that the swap valuation should be adjusted with a "quanto adjustment".So we have two methods that are both supposedly arbitrage free, but one has a quanto adjustment and the other doesn't. Are these two methods inconsistent, or have I missed something?

one contains the other as a special case with quanto adjustment = 0 (at least you can view it like this)

Thanks for the reply.But then which one is correct? Are you saying the Bianchetti version is generally correct, whereas the classical no arbitrage argument is only correct in some cases i.e. when the correlation or volatilities are 0? I don't understand why the normal argument wouldn't work in these cases.

QuoteOriginally posted by: dtrehaloseAre you saying the Bianchetti version is generally correct, whereas the classical no arbitrage argument is only correct in some cases i.e. when the correlation or volatilities are 0?yes, it depends on your model assumptions. What is the "normal" argument ? When your numeraire lives on a different curve than your forwards you estimate, you will in general get an adjusted forward.

The "normal" or simple argument is the one that I've seen most people use to justify OIS discounting. It usually goes something like this. If a swap is in the money to a bank, collateral will be posted. This collateral will gain interest at the daily SONIA rate. How much collateral should be posted? This should be the amount that will give the expected cashflow at maturity accounting for interest on the collateral. Hence, we have to use OIS discounting otherwise we would generate arbitrage opportunities.This seems like a fairly sound argument to me for OIS discounting. It implies the correct way for valuing a swap would be to use a LIBOR forwarding curve to generate cashflow and discount these on an OIS curve. But the Bianchetti argument implies that even this method is not correct and would still does not fulfil the no arbitrage argument, unless we apply a quanto adjustment. It is not intuitive to me why the above argument is wrong - why would having correlation between the SONIA and LIBOR rates create an arbitrage situation? The "simple" argument must be flawed somewhere, but I just can't see where.

Formally discount notion comes with zero coupon risk free bond. There is no other different definition of discounting or discount factor. Its also represents time value of unit of a currency. In other words this is a way to invest say $q at t and receive $1 at a future moment T. Such discount represents risk free bonds and LIBOR family contracts. Any swap rate does not match given definition of discounting. It is wrong to impossible to apply OIS rate to get in future known $C. OIS rates are probably close in value and positively correlated with T-bond or LIBOR rates therefore one can use them. Nevertheless it looks like a sort of manipulation in which one is trying to sell his products for a higher price than it should be.

QuoteOriginally posted by: list1It is wrong to impossible to apply OIS rate to get in future known $C. OIS rates are probably close in value and positively correlated with T-bond or LIBOR rates therefore one can use them. Nevertheless it looks like a sort of manipulation in which one is trying to sell his products for a higher price than it should be.Are you saying we shouldn't be using OIS discounting at all? The vast majority of swaps are valued on OIS curves these days...

QuoteOriginally posted by: dtrehaloseQuoteOriginally posted by: list1It is wrong to impossible to apply OIS rate to get in future known $C. OIS rates are probably close in value and positively correlated with T-bond or LIBOR rates therefore one can use them. Nevertheless it looks like a sort of manipulation in which one is trying to sell his products for a higher price than it should be.Are you saying we shouldn't be using OIS discounting at all? The vast majority of swaps are valued on OIS curves these days...dtrehalose, meet list!

You can use OIS as discount as far as others have done and next you can think what you are doing. You call OIS rate as a discount factor. It is reasonable to ask yourself what is by definition risk free discount factor. If you open old books you will find out that risk free discount factor is associated with risk free zero coupon bonds. In theory which we use to define basic notions we assume that such bonds are known for eact t and for all expiration dates T. In such setting you can calculate value of the c-coupon bonds which implies that at t we buy c bonds with expiration at the time of coupon payments. These two examples illustrate the sense and definition of the discount factor or discount rates. Similar for non US market one can use LIBOR or we theoretically can define coupon LIBOR contracts for which coupons should be apply LIBOR discount factor. The the question is whether or not to get $1 at T one should apply OIS discount rate at t. And next one should specify what actually OIS rate at t promises at T and in what degree OIS rate corresponds to discount rate.On the other hand primary mathematical properties of the OIS and discount rates are similar though values are a little bit different.It might be interesting to recall what formally LIBOR manipulation means ignoring the charging values. The problem was a small changes of deposit rates. Formally using OIS to form price of instruments has similarity that called manipulations in LIBOR case. Using OIS buyers pay higher price if sellers used T-rates or LIBORs.

List1....sorry I have no idea what you are talking about! How does this relate to my original question on whether an OIS discounted LIBOR swap needs a Bianchetti style "quanto" adjustment?

My remark does not related to a Bianchetti style "quanto" adjustment. I only tried to highlight the fact that OIS or other swap rates. Formally they do not represent discount rates.

fantastic - welcome back

Hi Dave, what is a definition of discount rate? One of the modern definition are1. The rate at which member banks may borrow short term funds directly from a Federal Reserve Bank. The discount rate is one of the two interest rates set by the Fed, the other being the Federal funds rate. The Fed actually controls this rate directly, but this fact does not really help in policy implementation, since banks can also find such funds elsewhere. also called Federal Reserve Discount Rate.2. The interest rate used in discounting future cash flowsThe first definition is good while the second suggests to call discount if it is used for calculation PV. Then the question is : how to specify which rates one can be used to calculate PV and which rates are not? For example, if OIS is a risk free why zero and non zero coupon bond does not use it? Whether OIS ( t , T ) represent date-t value of $1 at T?

QuoteOriginally posted by: list1Hi Dave, what is a definition of discount rate? One of the modern definition are1. The rate at which member banks may borrow short term funds directly from a Federal Reserve Bank. The discount rate is one of the two interest rates set by the Fed, the other being the Federal funds rate. The Fed actually controls this rate directly, but this fact does not really help in policy implementation, since banks can also find such funds elsewhere. also called Federal Reserve Discount Rate.2. The interest rate used in discounting future cash flowsThe first definition is good while the second suggests to call discount if it is used for calculation PV. Then the question is : how to specify which rates one can be used to calculate PV and which rates are not? For example, if OIS is a risk free why zero and non zero coupon bond does not use it? Whether OIS ( t , T ) represent date-t value of $1 at T?all good points...