# Yield Curve Vs. Swap Curve

#### Anthony_CHRIS

Hi All,

I am going through an exercise for a project and I am a bit at a lost with all the semantics around the yield curve (swap curve, libor rate, zero-coupon bond yield, T-Bill rate, etc.)

In the project, I am given the swap curve at different dates, and I want to calculate the yield curve from it. I am not sure how to approach this problem. Do I have to do it through some sort of derivative contract?

I'm not asking for a specific answer, just maybe some insight into the difference between those 2 curves.

Thanks

#### Ken Abbott

##### Managing Director
The classic version of this problem (which every finance student in the 90s had to do) is that you are given futures prices for the first n contracts and then are given a series of points further out. From this you have to derive forwards, discount rates, and ultimately yields-to-maturity for every point along curve.

• Anthony_CHRIS

#### Anthony_CHRIS

The classic version of this problem (which every finance student in the 90s had to do) is that you are given futures prices for the first n contracts and then are given a series of points further out. From this you have to derive forwards, discount rates, and ultimately yields-to-maturity for every point along curve.

Yeah, this clears it out.
I got confused when I looked up some online references and they use some terms interchangeably when they shouldn't. It seems this is common bad practice with all the difference interest rate curves one can derive.

#### Peter

A swap curve is to swaps as a yield curve is to bonds. Swap curves and yield curves represent similar types of data in the same kind of manner. They both give you the yield for a given maturity or tenor on the assumption that each point on the curve represents a contract made *right now*. In other words, the yield on a 2M debt made today, the yield on a 6M debt made today, the yield on a 5Y debt, made today, and so on.

It sound like you're given a different kind of information. It sounds like you're given the yield on a 2M debt made tomorrow, the yield on a 6M debt made next week, the yield on a 5Y debt made next month, and so on.

Sounds like the point of your problem is to turn statements like "the yield of a 5Y debt made next month" into a true statement about a debt made today, because once you do that, you can put that data into your yield curve.

#### Dweeb

Hi All,

I am going through an exercise for a project and I am a bit at a lost with all the semantics around the yield curve (swap curve, libor rate, zero-coupon bond yield, T-Bill rate, etc.)

In the project, I am given the swap curve at different dates, and I want to calculate the yield curve from it. I am not sure how to approach this problem. Do I have to do it through some sort of derivative contract?

I'm not asking for a specific answer, just maybe some insight into the difference between those 2 curves.

Thanks
Constructing a zero coupon term structure uses information from cash and derivative markets depending on liquidity. For example – 1 to 3 mth LIBOR, Futures strips to two years, and then interest rate swaps (IRS).

Implied spot rates are derived from Futures using PV and FV. IRS have implied coupons, so a spot zero coupon equivalent is derived. A zero rate should be higher than the implied coupon rate.

Caveats - some use the IRS term structure and don’t derive the zero rates. Then there is a convexity adjustment to true up the basis between Futures and IRS, plus upward/downward sloping curve issues.

All this was done from memory, so maybe I’ll stand corrected.

#### Anthony_CHRIS

Constructing a zero coupon term structure uses information from cash and derivative markets depending on liquidity. For example – 1 to 3 mth LIBOR, Futures strips to two years, and then interest rate swaps (IRS).

Implied spot rates are derived from Futures using PV and FV. IRS have implied coupons, so a spot zero coupon equivalent is derived. A zero rate should be higher than the implied coupon rate.

Caveats - some use the IRS term structure and don’t derive the zero rates. Then there is a convexity adjustment to true up the basis between Futures and IRS, plus upward/downward sloping curve issues.

All this was done from memory, so maybe I’ll stand corrected.

You are spot on. I ended up using IRS for all dates, although as you said it might not be such a good idea for short term payments. Also there is a MATLAB function called IRDataCurve that performs much of the tedious calculations for you. You only need to provide the appropriate historical rates.

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