I (still) have an issue with the discount curve.Take the example of a plain vanilla IRS 1Y vs 3M. To price it, you need the 3M forward curve, a good interpolation technique to compute the strip of FRAs, and a discount curve. For the sake of simplicity, we assume that the market prices off a same 3M forward curve and uses the same interpolation technique. The only difference between the dealers will be the discount curve. But the choice of the discount curve has an impact on the value of the IRS: dealer A chosing to build his discount curve from OIS will not find the same value as dealer B who builds his discount curve based on BOR rates. For one, the IRS may be exactly at par while for the other it may not.Here is the paradox:1) If we consider each dealer uses his own discount curve, how can IRS markets be so orderly (tight spreads, all market-makers quoting very similar bid-ask) as they would all compute different values for the IRS?2) If we consider all players use the same discount curve, then of course they would quote the same price, but their valuation would be distorted. Unless I am wrong, the discount curve is supposed to answer the question: what is $1 worth in X time? The answer necessarily varies among dealers: a dealer with access to a term deposit will find $1 is not worth the same thing in X time than a dealer internally refunded at a spread below overnight rate.Is this the answer:A) The market has agreed on a convention for the discount curve based on the fact that a) at payment date each cash-flow will be worth its nominal value so only the "path" to this value differs, not the value in itself, and b) once paid, no one can predict what will be the effective forward interest rate each of these future cash-flows will go through (who knows how and when the flows received will themselves be reinvested) until the last one is paidB) Say each dealer computes IRS himself, differences in prices among dealers can be split upon the forward curve, the interpolation technique and the discount curve; depending on which two the dealer wants to keep unchanged, the 3rd parameter can be adjusted so that the value of the IRS stays the same (this is called calibrating the pricer).All comments, criticisms and "enough with rate curves!' are welcome.Caracole.

You are confusing model and reality.The observed prices are real. Dealers are setting these prices in a way that makes sense for their business and the markets in which they participate. They may be using Oiuja boards to set these prices, but you will never know.Since you do not really know how these prices are set, you have applied a model. This model should have some basis in reality and feel "real". But since you have made it up, it will not exactly fit with reality. The paradox lies with you, not the dealers or the markets. It's like selecting a vehicle fuel economy model that seems to work pretty well, then obsessing because your model says red cars should have worse economy, yet they don't. They don't because your model is unreal, not because there is a problem with the vehicle.Then your question is, "How do I safely use an unreal model?"

The mkt is not orderly... Certainly, not these days.

Thank you for your replies.@ClosetChartist, I understand your point, that the model should be tweaked to stick to the reality (the price). But do you agree that both the strip of standard FRAs and the discount curve are reality, not model (only the interpolation is a model here), or do you consider that the discount curve is part of the model as well? The reason I say the FRAs and the discount curve are reality is because you can observe standard FRAs prices in the market + you know your financing constraints and can build the discount curve based on them.

QuoteOriginally posted by: Caracole Here is the paradox:1) If we consider each dealer uses his own discount curve, how can IRS markets be so orderly (tight spreads, all market-makers quoting very similar bid-ask) as they would all compute different values for the IRS?I don't see any paradox, the market is collateralised so that is the funding rate.If you want to delve deeper there are advantages to managing your exposures in different currencies but that is a second order effect.

It's a complicated subject these days and I understand your confusion, caracole... Reality is that the mkt is not orderly and has gotten extremely non-fungible. So there are, in fact, all sorts of issues arnd discount curves and collateral. The solution, which is currently being implemented quite aggressively, involves a transition to central clearing.

The fact is that risk-neutral (i.e. traditional sell side) models are not used to predict the market moves or to confirm your current view. They are the interpolators, in a large sense of it. View them as black boxes (sorry for over-used terminology) with many inputs and single output of instrument PV, where the inputs can be other (hedging) instrument prices. So in a way, models are only there to predict primary instrument prices in relation to the hedging instrument prices. This setup works both for vanilla and exotic products.