Hi All,I need some help with the attached derivation of a zero coupon discount factors curve.Basically, I have a 3 month floating rate, with 3 IR futures out to the end of year 1. This is followed by 3 Swap rates for years 2,3,4For the Cash Rate and the futures, I have used the forward period rates to determine the discount factor over the period. This looks to be correct for each of the three month periods. However, when I start deriving the discount factors with the Swaps, I am getting some crazy forward rates.I am using the formula 1-Swap Rate * (sum of previous DF) / (1-Swap Rate) Could anybody shed some light on what I doing wrong...or recommend any website/book that might help me?I attach file that shows workings...This is from a previous exam paper so any thoughts would be great...Thanks alot...

You have to add the quarterly flows. You do that for the first year, but then you only add one flow per year. And you have to divide the swap rate by four.So insert three rows between each of your years, for period 1.25, 1.5, 1.75; then 2.25 and so on. Then divide the stated swap rate by 4 before using it in your formula. That should give you the correct answer.

Thanks Aaron,I have redone using your suggested method. Some of the Forwards at the 2,3,4 intervals look large in comparison to the other forwards. Is there any possible explanation??...Also, is it also possible/correct to calculate the first years compound "yearly" rate using the quarterly forwards rates implied by the futures. And then use (1/(1+r)) to calculate the first DF. I could then use the ( 1-Swap Rate * (sum of previous DF) / (1-Swap Rate) ) formula to calculate the DF for the Swap rates...Please see attached for example....Many Thanks

hiyou need to work out discount factors for all the maturities provided. for the deposit the df is given bydf = 1/(1+R*T) where T = 0.25for the futures, you work out the df at the maturity of the future given the df at the start using the implied rate from the futures pricedf2 = d1f * 1/(1+RT) where T = 0.25 and R is the implied rate given by 1-Ffor the swaps you need to work out the discount factor for the last swap flow as you have the intermediate ones. I dont think you need to assume quarterly as the question does not say and annual is good enough. hence from the par swap relation we know that1 = R * df1 + R * df2 + .. (1+R) * dfn where R is the swap rate and I have assume that interest is paid annuallyhence the dfn is given by:dfn = ( 1 + R*df1 + R*df2 + .. + R*df(n-1))/(1+R)using the above I get the following set of discount factors:Term Swap Rate/Fut Rate Interest Payment DF Zero Rate (CC)0.25 3% 3% 0.750% 0.99256 2.99%0.5 97 3.00% 0.750% 0.98517 2.99%0.75 96.6 3.40% 0.850% 0.97686 3.12%1 96.8 3.20% 0.800% 0.96911 3.14%2 3.25% 3.25% 0.93802 3.20%3 3.50% 3.50% 0.90169 3.45%4 3.75% 3.75% 0.86233 3.70%once you have your zero rates interpolate for the maturities you need to calculate forward rates.

Thanks Daveangel, that's great!One final question, the formula 1 = R * df1 + R * df2 + .. (1+R) * dfn, when changing over from the final future of the first year (the final quarter) to the first Swap rate...I should include the DF for that period in the above formula (correct??) Whereas if a question consisted of standalone Swaps with no futures I would use (1/(1+R)) for the first Swap and then for the second Swap rate but the discount factors in the above formula would consist of ( DF1 = 1 ) + ( DF2= 1/(1+R) )Example attached..Thanks Again!

QuoteOriginally posted by: iwright218Thanks Daveangel, that's great!One final question, the formula 1 = R * df1 + R * df2 + .. (1+R) * dfn, when changing over from the final future of the first year (the final quarter) to the first Swap rate...I should include the DF for that period in the above formula (correct??) yes - it doesnt matter where you discount factors come from so long as they are appropriate in terms of credit risk etc. for the first swap there are two cash flows. one at end of year 1 and the second is at the end of year 21 = R * df1 + (1+R)*df2no you solve for df2df2 = ( 1 - R*df1) /(1+R)then you go to the second swap which matures in year 31 = R * df1 + R * df2 + (1+R) * df3and solve for df3.