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ggcroco
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Joined: September 22nd, 2006, 7:44 am

yield curve with strip IR futures

September 22nd, 2006, 8:46 am

Hi everybody,I'm trying to build a yield curve using IR futures for the short term part. If you consider End Date as the future settlement date + 3 months, you can calculate the discount factor for this date as follow:DF_enddate = DF_settlementdate * 1/(1+(100-FutPrice) * (EndDate - SpotDate) / Basis) ( * )Often, for one futures maturity you have DF_settlementdate = DF_enddate of the previous future.But sometimes, you can have EndDate_previousfuture < SettlementDate_currentfuture or on the contrary EndDate_previousfuture > SettlementDate_currentfuture. In this case you can't apply (*), any of you have an idea to solve this problem ???Thanks in advance for your answer!G
 
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Gamanti
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Joined: February 25th, 2003, 7:30 pm

yield curve with strip IR futures

September 22nd, 2006, 1:02 pm

You're probably calculating the dates wrongly. Futures are designed so not to have gaps. The error might be generated by one of the following:1) you need to look at the underlying deposit Start/End dates, not the futures expiry. So for example Eurodollar futures are linked to a 3M libor deposit starting on the 3rd wed of the expiry month. The futures expires 2 business days prior (Since Libor settles T+2)2) Maybe you are calculating the Libor End date wrongly, something is wrong with your daycount conventions?Anyway, to double check your dates, you can use bloomberg, these are the fields: FUT_LAST_TRADE_DT INT_RATE_FUT_START_DT INT_RATE_FUT_END_DTEDZ6 Comdty 18-Dec-06 20-Dec-06 21-Mar-07EDH7 Comdty 19-Mar-07 21-Mar-07 20-Jun-07EDM7 Comdty 18-Jun-07 20-Jun-07 19-Sep-07EDU7 Comdty 17-Sep-07 19-Sep-07 19-Dec-07EDZ7 Comdty 17-Dec-07 19-Dec-07 19-Mar-08EDH8 Comdty 17-Mar-08 19-Mar-08 18-Jun-08EDM8 Comdty 16-Jun-08 18-Jun-08 17-Sep-08EDU8 Comdty 15-Sep-08 17-Sep-08 17-Dec-08EDZ8 Comdty 15-Dec-08 17-Dec-08 18-Mar-09EDH9 Comdty 16-Mar-09 18-Mar-09 17-Jun-09EDM9 Comdty 15-Jun-09 17-Jun-09 16-Sep-09EDU9 Comdty 14-Sep-09 16-Sep-09 16-Dec-09EDZ9 Comdty 14-Dec-09 16-Dec-09 17-Mar-10EDH0 Comdty 15-Mar-10 17-Mar-10 16-Jun-10EDM0 Comdty 14-Jun-10 16-Jun-10 15-Sep-10EDU0 Comdty 13-Sep-10 15-Sep-10 15-Dec-10EDZ0 Comdty 13-Dec-10 15-Dec-10 16-Mar-11EDH1 Comdty 14-Mar-11 16-Mar-11 15-Jun-11EDM1 Comdty 13-Jun-11 15-Jun-11 21-Sep-11EDU1 Comdty 19-Sep-11 21-Sep-11 21-Dec-11EDZ1 Comdty 19-Dec-11 21-Dec-11 21-Mar-12EDH2 Comdty 19-Mar-12 21-Mar-12 20-Jun-12EDM2 Comdty 18-Jun-12 20-Jun-12 19-Sep-12EDU2 Comdty 17-Sep-12 19-Sep-12 19-Dec-12EDZ2 Comdty 17-Dec-12 19-Dec-12 20-Mar-13EDH3 Comdty 18-Mar-13 20-Mar-13 19-Jun-13EDM3 Comdty 17-Jun-13 19-Jun-13 18-Sep-13EDU3 Comdty 16-Sep-13 18-Sep-13 18-Dec-13EDZ3 Comdty 16-Dec-13 18-Dec-13 19-Mar-14EDH4 Comdty 17-Mar-14 19-Mar-14 18-Jun-14EDM4 Comdty 16-Jun-14 18-Jun-14 17-Sep-14EDU4 Comdty 15-Sep-14 17-Sep-14 17-Dec-14EDZ4 Comdty 15-Dec-14 17-Dec-14 18-Mar-15EDH5 Comdty 16-Mar-15 18-Mar-15 17-Jun-15EDM5 Comdty 15-Jun-15 17-Jun-15 16-Sep-15EDU5 Comdty 14-Sep-15 16-Sep-15 16-Dec-15EDZ5 Comdty 14-Dec-15 16-Dec-15 16-Mar-16EDH6 Comdty 14-Mar-16 16-Mar-16 15-Jun-16EDM6 Comdty 13-Jun-16 15-Jun-16 21-Sep-16EDU6 Comdty 19-Sep-16 21-Sep-16 21-Dec-16The first date is the Futures Expiry, the second date Libor start and the last one libor end date for each and every Euro$ contract. Note How FutureEnd(i)=FutureStart(i+1)
 
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ggcroco
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Joined: September 22nd, 2006, 7:44 am

yield curve with strip IR futures

September 22nd, 2006, 1:21 pm

Well, actually, I think your 2 proposals are right, I think that I m doing a mistake in my daycount convention, because I don't take into account the fact that the futures are linked to 3month euribor (or libor). Then, I don't calculate properly their deposit dates!Then, I am going to fix it, following the rule you gave me, I believe it will work accodring IMM rules.Thx a lotG
 
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Jim
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Joined: February 1st, 2002, 5:20 pm

yield curve with strip IR futures

September 22nd, 2006, 4:50 pm

No, Bloomberg (and Gamanti) is wrong. The ED futures coverge to a price equal to 100 minus the LIBOR 3-Month rate whose value date is the 3rd Wednesday in the contract month. As ggcroco correctly points out, the maturity of the LIBOR rate to which the future converges is often NOT the 3rd Wednesday corresponding to the next quarterly contract. How you deal with this detail is up to you.You can ignore this detail and build you curve so that there are no gaps or overlaps. But then you have shifted this problem onto your pricers. For example, swaps with quarterly, non-imm accrual periods which happen to fix on the same day as the futures expiry with be misvalued because their accrual periods won't match all of the IMM dates.Alternatively, if you are doing bootstrapping to build your curve, you can interpolate/extrapolate to get the DF_settlementdate and then use the simple interest formula to fix your DF_enddate.In general, what you want out of your curve model is that you pricing model works correctly. Whatever your pricer is doing for a rate fixing on the same day as the future's expiry is what your curve model should do so that you get the right fixing rate into your pricer.
 
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ggcroco
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Joined: September 22nd, 2006, 7:44 am

yield curve with strip IR futures

September 25th, 2006, 6:00 am

Hi Jim,Thanks for your point of view ! As you point out, what 's the most important is to have a pricer which gives you the correct prices ! So, I think I m going to consider my yield curves in different ways, depending on the kind of interest rates derivatives I want to price (accodring to their own rules).Thx