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Why Bond Futures Are Difficult to Price from Deposit Rates

Article Quant Q&A · Author: endian
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Summary

The document explains why a two-year government bond future cannot be priced reliably by chaining deposit futures to estimate a matching interest rate. A deposit curve can be built from deposit rates and used to discount the bond’s cash flows, but deposit rates may differ from government bond rates because of term and credit premiums and cash-market effects. These differences limit the usefulness of the resulting bond valuation.

For futures, the key pricing link is the repo value of the cheapest-to-deliver bond in the delivery basket. The delivery process can also give the futures contract an embedded option: changes in interest rates may change which bond is cheapest to deliver, affecting the futures price. The answer describes market practice as pricing bonds from futures after accounting for repo. It offers a conceptual explanation rather than a numerical pricing recipe; it does not specify how to estimate adjustments or value the delivery option.

Key ideas

  • Deposit rates can be used to construct a discount curve for valuing bond cash flows.
  • Deposit and government bond rates can diverge because of credit, term, and cash-market premiums.
  • A bond future’s value is strongly linked to the repo economics of the cheapest-to-deliver bond.
  • The delivery basket creates optionality because the cheapest-to-deliver bond can change with interest rates.
  • Practical valuation requires accounting for repo and delivery mechanics.

Tags

Fixed incomeFuturesDerivatives pricing
Full text
# Pricing a bond future with a basket of deposit futures


# Pricing a bond future with a basket of deposit futures












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.

## Answer by David (score 2, accepted)

https://quant.stackexchange.com/a/2973

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.