# Why are multiple custom curves (swap) built for one desk?

Currently in a journey of learning and getting my hands a bit dirty with Interest Rate Swaps.

1. Why there are multiple customized curves built by many even within one desk? For e.g. Short Rates desk and FI desks seem to have multiple curves of their own.

2. What are the usually accepted underlying securities and rates building these curves?

3. I also came across with the jargon and questions like "Forecasting curves". What does it mean by forecasting curve? (opposed to a discounting curve). Is it something like calculating floating leg's cash flows using forward rate?

## Chapter 1: Goldilocks is ousted by the bears

Once upon a time, the banks used a fixing called LIBOR as a measure of the risk-free interest rate. Then the big hairy crisis came along and ate all our assumptions, leaving just the bones of the fixing (upon which everything else still fixes) and the mantle of risk-free rate proxy was passed on to a family of Overnight fixings, called Sonia, Eonia and -ahem- FedFundEffective.

Since everything (e.g. FRAs, 3m Interest Rate Futures, OTC IRS, Deliverable Swap Futures, cross-currency basis swaps, 3m-OIS basis, etc) still fixes on LIBOR (or other xIBOR depending on the currency), the questions now are:

1. What do you expect the xIBOR fixing to be for any given term?
2. What do you expect the Overnight fixing to be for any given term?
3. How much is your CVA desk going to charge you to cover the credit risk?

So to value a forward-starting IRS, I need both an Overnight curve for discounting, but also a curve of forecasted fixings to estimate the cash flows themselves. When there was 1 curve, it was far simpler.

Summary: Once there was 1 fixing, and it was a proxy for the risk free rate, so there was 1 curve of discount factors. Now it is no longer such a proxy, but because liquid instruments fix on these other fixings, you have to build curves to work out what those fixings are expected to be as well.

-- Edit for great good and new RFR --

## Chapter 2: Goldilocks returns

Regulatory changes (viz: the ARRC, EMIR, the BoE) have deemed that even the mantle of Libor (and cousins Euribor, etc) must now be offered up to the be burnt in the witch's oven. So instead of having a 1m Libor, 3m Libor and 6m Libor curves, the instruments which use those fixings must be replaced by new RFR (Risk Free Rates, or, Daughter of Goldilocks).

This is a return to the single curve world - all your multicurves are belong to RFR. FedFunds is being replaced (in usage) by a comfy SOFR, Eonia by the inpronouncable €STR (in October 2019) and TOIS has already become SARON. Sonia is dead, long live Sonia.

# Chapter 2.5: Goldilocks and the mirror

Goldilocks II gives us backward looking 'in arrears' fixings - they are fixed in light of actual trades. This is in contrast to the forward-looking originals in Libor and Euribor.

Once Goldilocks II returns and kills all the bears (prophesied to be 2022), there is still a shadow in the wings (I mean, how else can we make the 3rd and 4th films of the trilogy): the buy side and the FI markets both want a forward looking fixing like the fixing they once knew, so they may well make up a sister fixing to Goldilocks II, a mirror fixing which looks forward. This would then be either a second curve or a lag adjustment.

So in summary, most of the textbooks were written during Goldilocks I's reign, some have since been written during the Bear Junta, and the next chapter is as yet unwritten.

• Learning via melo-drama can't get any better : quoting mantle of risk-free rate proxy was passed on to a family of Overnight fixings, called Sonia, Eonia and -ahem- FedFundEffective... Coming back to the main intention of my question, sometime back I used this as my first tutorial with some background reading based on CFA L1, Fabozzi, Tuckman and Derivatives Demystified. Those materials helped alot in order to understand the basic concepts. – bonCodigo May 23 '14 at 12:44
• Aren't the forecasting fixing rates are infact the forward rates? Because that's what we used to derive the future cashflows of floating leg? – bonCodigo May 23 '14 at 12:53
• Yes, unless you have more context, I would expect a forecasting curve to be the same as a forward rate curve. The difference is that you don't have to make it into a DFC any more, and that you may only use 3m-fixing products together or 1m-fixing products. Once upon a time it was Cash, Futures, Swaps; these days if the swaps are 6m, those are 3 different curves. – Phil H May 23 '14 at 14:25
• What are you referring by "more context"? Further can you define the jargon DFC (discount factor curve perhaps)? Quoting: The difference is that you don't have to make it into a DFC any more, and that you may only use 3m-fixing products together or 1m-fixing products. This is not clear to me.., >.< Does it mean steps for boostrapping for stripping off forward rates to build swap curve goes down by 1 step? – bonCodigo May 23 '14 at 15:14
• DFC is Discount Factor Curve, where you represent the term structure of rates as a set of discount factors. Classically, you would do this so that you can calculate say a 1m forward rate (even though the inputs were 3m rates) and so on. Now, however, you only care about what the fixing will be, so you don't need to bother with a DFC. The discounting is done using the OIS curve, so the bootstrapping is far simpler than a classical curve. – Phil H May 27 '14 at 6:36