I am trying to explore the relationship between a plot of a Libor forward curve of a curtain tenor and the same of a swap rate. I see that the latter 2 are the same for 3 month tenor, which is clear why from the definition of one peroid payment. However, once I plot the same for the tenor of say 10Y, I see that swaprate curve is quite above the forward rate. Would like to see if the line of thought below is correct.In the US convention, when ask for 10Y swap rate, that means that a swap rate is computed from the swap with float side 3 month Libor paid every 3 months and fixed side is semiannual, while the payments happen over the period of 10 years? So, the swap rate would be some weighted average of the 3 month Libor over the next 10 years for every single point in time on the curve, so my expectation of the 3M forward average rate. The 10Y forward rate, is the rate to invest for 10 years, which must be above any 3M forward rate by the assumption of th eupward sloping spot rate curve.

It's not clear what your forward curve really is...

This is the LIBOR curve that I see on the Boomberg screen for a certain tenor upon request. QuoteOriginally posted by: MartinghoulIt's not clear what your forward curve really is...

Still don't quite understand... In your fwd curve plot, what exactly are the axes?

On 3 month Forward libor, it is the value of the forward rate vs future time in years.QuoteOriginally posted by: MartinghoulStill don't quite understand... In your fwd curve plot, what exactly are the axes?

So on the same plot which has time T along the X axis you're showing two things: a) the rate for a swap with maturity T; and b) the rate for a 3M FRA, start T-3m, end T. Is this correct?

YEs, the only thing is I am not sure as I would thought by maturity of a swap it is meant to be the swap starts paying at time "T" for a certain tenor, say for the next 10 years. And for the forward rate this is the FRA rate to borrow money at time "T" for 3 months. But I might be mistaken. QuoteOriginally posted by: MartinghoulSo on the same plot which has time T along the X axis you're showing two things: a) the rate for a swap with maturity T; and b) the rate for a 3M FRA, start T-3m, end T. Is this correct?

QuoteOriginally posted by: Kamil90YEs, the only thing is I am not sure as I would thought by maturity of a swap it is meant to be the swap starts paying at time "T" for a certain tenor, say for the next 10 years. And for the forward rate this is the FRA rate to borrow money at time "T" for 3 months. But I might be mistaken. QuoteOriginally posted by: MartinghoulSo on the same plot which has time T along the X axis you're showing two things: a) the rate for a swap with maturity T; and b) the rate for a 3M FRA, start T-3m, end T. Is this correct?Sorry, I don't understand the bit about the swap...

What I mean by a plot of the forward swap rate curve is the following: take a case of the swap with a term of 10 years, that is, one side pays 3 month libor over 10 years every 3 months and another side pays a fixed side twice per year for 10 years. Then I can calculate what is this fixed number is, i.e. what is 10 year spot swap rate(provided I have a Libor 3M curve and a discounting curve). Now I consider the case of the same swap that starts in T=1 year and not today(T=0), then it will be a forward swap rate which has some value for T=1 year. So, for each fixed T(0<T<50 yrs) I can create a set of values of forward 10 year swap rates. Thus, my plot is: x axis is T and y axis is the value of a forward swap rate(at T=0 it is a spot swap rate in fact).

I know how swaps work and I also understand now that for every time T on the X axis you're plotting the 10y fwd rate out of time T. But you're also plotting something else in the same graph, if I am not mistaken. What is that other thing that you're plotting exactly?

So, this is one of the curves: another one, which I see above the forward swap curve is a 10Y forward curve, that is at every time T I can borrow money at this rate for the time period of 10 years. This is my 10 year forward rate curve. QuoteOriginally posted by: MartinghoulI know how swaps work and I also understand now that for every time T on the X axis you're plotting the 10y fwd rate out of time T. But you're also plotting something else in the same graph, if I am not mistaken. What is that other thing that you're plotting exactly?

QuoteOriginally posted by: Kamil90So, this is one of the curves: another one, which I see above the forward swap curve is a 10Y forward curve, that is at every time T I can borrow money at this rate for the time period of 10 years. This is my 10 year forward rate curve. QuoteOriginally posted by: MartinghoulI know how swaps work and I also understand now that for every time T on the X axis you're plotting the 10y fwd rate out of time T. But you're also plotting something else in the same graph, if I am not mistaken. What is that other thing that you're plotting exactly?Right, so the second plot shows the zero coupon 10y rate out of every date T?

Kamil,Is my understanding of what you are plotting correct:1. Forward curve, the rate to borrow for 3 months at point "T"2. (Use the above forward curve to calculate) The rate of a forwarding starting swap, i.e. the 10y swap rate starting at time "T".Your question is:Why is 10y rate of a swap starting at time T higher than the 3 month rate at time T?Your own explanation:[quote]In the US convention, when ask for 10Y swap rate, that means that a swap rate is computed from the swap with float side 3 month Libor paid every 3 months and fixed side is semiannual, while the payments happen over the period of 10 years? So, the swap rate would be some weighted average of the 3 month Libor over the next 10 years for every single point in time on the curve, so my expectation of the 3M forward average rate. The 10Y forward rate, is the rate to invest for 10 years, which must be above any 3M forward rate by the assumption of th eupward sloping spot rate curve.[/quote]The forwarding starting swap rate with 10y maturity is higher than the 3-month forward rate because of upward-sloping spot rate curve

Yes, this is precisely what 10 year forward curve means, at any time T this it shows the spot rate for the next 10 years.QuoteOriginally posted by: MartinghoulQuoteOriginally posted by: Kamil90So, this is one of the curves: another one, which I see above the forward swap curve is a 10Y forward curve, that is at every time T I can borrow money at this rate for the time period of 10 years. This is my 10 year forward rate curve. QuoteOriginally posted by: MartinghoulI know how swaps work and I also understand now that for every time T on the X axis you're plotting the 10y fwd rate out of time T. But you're also plotting something else in the same graph, if I am not mistaken. What is that other thing that you're plotting exactly?Right, so the second plot shows the zero coupon 10y rate out of every date T?

No, I don't think 10 year swap curve is higher, in fact it is not, it is rather exhibits a behavior of a "moving average" for the Libor 3M forward curve. However, 10 year forward curve is above all of these. But I think I understood the relationship between the curves already...QuoteOriginally posted by: eurokopekKamil,Is my understanding of what you are plotting correct:1. Forward curve, the rate to borrow for 3 months at point "T"2. (Use the above forward curve to calculate) The rate of a forwarding starting swap, i.e. the 10y swap rate starting at time "T".Your question is:Why is 10y rate of a swap starting at time T higher than the 3 month rate at time T?Your own explanation:[quote]In the US convention, when ask for 10Y swap rate, that means that a swap rate is computed from the swap with float side 3 month Libor paid every 3 months and fixed side is semiannual, while the payments happen over the period of 10 years? So, the swap rate would be some weighted average of the 3 month Libor over the next 10 years for every single point in time on the curve, so my expectation of the 3M forward average rate. The 10Y forward rate, is the rate to invest for 10 years, which must be above any 3M forward rate by the assumption of th eupward sloping spot rate curve.[/quote]The forwarding starting swap rate with 10y maturity is higher than the 3-month forward rate because of upward-sloping spot rate curve