UK Treasury Bill Discount Yields Versus Short Spot Rates

Summary

The document distinguishes two UK short-rate series that may appear similar but represent different quantities. Treasury bill observations are described as average discount rates from weekly tenders for 91-day bills. The government curve’s three-month spot rate, by contrast, is produced from a fitted theoretical curve and uses repo rates at the short end. The curve rate is continuously compounded, while the bill figure is a discount yield, so their quoted values need not match directly.

For historical short-rate modeling, the answer favors repo-based curve rates because it characterizes the UK bill market as relatively illiquid, while suggesting that either series may produce similar results in practice. That is a qualitative recommendation, not a backtest or calibration comparison, and the document does not detail conversions between discount yields and continuously compounded rates. The appropriate input therefore depends on the model’s intended rate definition and the market instrument being represented.

Key ideas

• Treasury bill observations reflect discount rates from weekly tenders for 91-day bills.
• Short spot rates come from fitted government curves and use repo rates at the short end.
• Bill discount yields and continuously compounded spot rates use different conventions.
• The answer prefers repo-based curve rates because it describes the UK bill market as relatively illiquid.

Tags

# Difference between a 3-months UK nominal spot rate and a 3-months UK treasury bill discount rate?


# Difference between a 3-months UK nominal spot rate and a 3-months UK treasury bill discount rate?












I am trying to collect data I could use for calibration of a short-rate modeling process, so I need data which represents the historical short-rates.

On the Bank of England webpage I came across the historical Government liability curve data, and also the 3-months UK treasury bills discount rates.

It turns out they are not the same. For example, on the 31 May 2017 the UK nominal 3-month spot rate was 0.04, and the 3-months UK treasury bill discount rate was 0.0575. Also, in the 3-months UK nominal spot rate table, values of 3-months spots are actually mostly not given.

I don't understand what is the difference between these two values, and which ones should I use for my historical data?

Many thanks for any insights on this.

## Answer by Helin (score 2, accepted)

https://quant.stackexchange.com/a/35046

The Treasury bill rates are actual yields of short-term Treasury bills. More precisely, these are "average rates of discount at the weekly tender for 91 day bills."

By contrast, the spot rates are calculated from theoretical fitted curves. Notable, the government curves use repo rates at the short end, not bill rates. Additionally, these are continuously compounded rates, not discount yields.

It is unlikely that you'll get very different results using either rates. I would opt for repo rates, primarily because the bill mkt in the UK is not particularly liquid.

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.