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I have a future on a two-year UK government bond that I wish to price. The bond future expires in 3 months. I was thinking of building a portfolio of 3-month deposit futures (1 x 3 month deposit starting in 3 months, 1 x 3 month deposit starting in 6 months and so on out to 2 years + 3 months). My intuition leads me to think that when the bond future expires, its 2 year interest rate should be equal to the 2 year interest rate implied by the deposit portfolio, but I suspect I need to make some adjustments to take in to account the semi-annual coupon paid by the bond.

Am I thinking along the right lines? Fixed income isn't something I have a massive amount of experience with.

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1 Answer 1

Unfortunately it's not so straight forward.

Let's deal first with pricing the bonds from cash deposits:

The procedure would be to build a discount curve from the deposit rates (many different ways to do this) and then use discount factors derived from your curve to discount the bonds cash flows to get it's present value. The curve you built would need to be adjusted to take account of: term premium, credit premium (deposits more risky the govt bond) and technical factors in the cash market like 'the turn' where companies require cash at important dates for balance sheet dressing. So with all those adjustments the chance of coming up with a sensible answer is practically zero so it's best just to use the market rates of the bonds and accept them as is.

Pricing a bond future from the price of the bonds in the delivery basket also requires some care. The futures price is largely determined by the repo value of the CTD (cheapest to deliver) bond from the basket. Also, due to the way the price of the delivered bond is calculated the CTD (cheapest to deliver) bond can change - this creates some optionality often referred to as the 'embedded delivery option'. This can become valuable in certain interest rate scenarios and affect the price.

This book has a pretty good treatment IIRC The Futures Bond Basis

So it's not really practical to price a bond future from cash deposit rates. What happens in practice is that the bonds are actually priced from the futures after taking the repo rate into account.

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Thanks, I appreciate your answer. I wasn't looking to price futures from cash deposits, but to price a future on a bond from a basket of futures on shorter-term deposits. I may open another question (or edit this one) to clarify what I'm looking to do. –  endian Feb 25 '12 at 23:01

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