Apologies to rocket scientists in advance but maybe a swaps dealer can help explain my "odd" results with a research project.I've been using high frequency indicative quote data (at one minute intervals) to determine the fair swap rate for the 1 yr sterling interest rate swap (quarterly payments, 3m Libor) from midquotes for short sterling futures and sterling FRAs. I use Libor midquotes to obtain my discount factors.Using data from mid-June 2002 to mid-June 2003, I find that my fair swap rates are invariably below the actual swap rate by 5 to 10 basis points (heavily concentrated around 7 bp), whether I use futures (linearly interpolated) or FRA quotes. My estimate of the convexity adjustment is around 0.4 basis points using the Burghardt & Hoskins method and can be ignored (the Ho & Lee approach yields a similar figure).Here is an example using FRA data from 10am, 20th June 2002:3m Cash 4.10%, 3x6FRA 4.47%, 6x9FRA 4.795%, 9x12FRA 5.065%3m Libor 4.10%, 6m Libor 4.28%, 9m Libor 4.47%, 12m Libor 4.64%Estimated fair swap rate = 4.60%Actual swap rate 4.70%I'd expected that both FRAs and futures would yield a fair swap rate close to the actual swap rate. A persistent gap of 5-10 bp is somewhat surprising.Any insights would be appreciated.

Market standard 1yr GBP swap is annual act365 vs 3m libor, so you need to calculate an annual swap rate. All other GBP swap rates are semi/semi act365

estcourt is correct. I ran the numbers quickly and the correct annual pay 1-year swap rate is just slightly under 4.7%. The difference between annual pay and semi-annual pay 1-year swaps is slightly more than 5 basis points.

Estcourt and DavidJ,Thanks for the help. I've found it difficult to locate references dealing with GBP swaps.I presume the adjustment is as simple as (1+0.0460/4)^4 - 1 = 0.0468 ? Please advise if I'm mistaken.Cheers

Here are some rough numbers. Using the Sterling cash rate and the FRAs, the discount factor at the end of 1 year is about 0.955229490. Using the FRN method the present value of the floating side per dollar notional is about (1.0 - 0.955229490) = 0.044770510. Dividing this by the fixed side cumulative discount factor (which in this case is the same as the 1-year discount factor because there is only one annual payment) gives the zero NPV fixed rate as (0.044770510/0.955229490) = 0.04686885, which rounds to 4.7%.

Actually, there is a classic book on Sterling swaps by Miron and Swannell called "Pricing and Hedging Swaps", published in the early 1990's by Euromoney books. No idea if its still in print.

Quote I use Libor midquotes to obtain my discount factorsI think this is your problem. Short sterling futures and sterling FRAs fix off of the LIBOR rate, not the midpoint between LIBOR and LIBID. The BBA website http://www.bba.org.uk/excel/libor/Jun02.xls has the following 11:00 am fixings for GBP LIBOR: 3M = 4.18219, 6M = 4.36125, 9M =4.55875, and 12M =4.72. These rates are more consistent with the FRA quotes. Also,combined with the fact that the 3M fixings for Jun 19, 20, and 21 are 4.19, 4.18219, and 4.17 (which are tightly grouped indicating little movement), tells me you have your cash rates wrong.

I just received this brand new from www.euromoney.com the other day. It is very much still in print and it is very much still expensive(135 pounds).QuoteOriginally posted by: DavidJNActually, there is a classic book on Sterling swaps by Miron and Swannell called "Pricing and Hedging Swaps", published in the early 1990's by Euromoney books. No idea if its still in print.

Thanks to all correspondents.I've had a copy of Miron and Swannell on my desk for several weeks. On closer reading I find an example in one of the later chapters assumes the fixed leg payment of the 1yr GBP swap is made annually. I now realise that this is what DavidJN and estcourt were driving at. I had assumed that fixed leg payments were made quarterly.Back to my SAS programme!Cheers