Converting Simple Deposit Rates to Displayed Zero Rates

Summary

The document addresses why a short cash instrument’s quoted fixing rate, a bootstrapped zero rate, and a displayed Bloomberg curve value may not appear to agree. The explanation is that the displayed zero curve converts from simple discounting on an ACT/360 basis to continuous compounding on an ACT/365 basis. Applying the displayed zero rate with continuous compounding over the stated ACT/365 period reproduces the indicated discount factor.

The response distinguishes this displayed value from the curve’s backend construction: the visible rate is described as being for display, while stripping uses the day-count convention applicable to the deal. This is a narrow convention-conversion example, not a full account of cash curve bootstrapping. The exact result depends on the instrument’s conventions and the relevant dates.

Key ideas

• A displayed zero rate can differ from a quoted cash fixing because their compounding and day-count conventions differ.
• The example converts simple ACT/360 discounting to continuous compounding on ACT/365.
• The displayed zero rate can reproduce a discount factor when applied using its stated convention.
• Backend curve stripping uses the day-count convention applicable to the deal.

Tags

# How does Bloomberg bootstrap CASH Instruments?


# How does Bloomberg bootstrap CASH Instruments?












Given the following datas :

If we do the bootstrap methodology for CASH Instrument we gotta :

Calculate the DF associated to the Market Quoted Rate (2.91157). For the 3M Fixing we have : T = 0.26115.

So the DF for this Market Quoted Rate is :

Then we can deduct the ZC Rate :

Which obviously does not match the Zero Rate shown in SWPM : 2.94084%

However doing :

Am I missing something or is Bloomberg SWPM Curve wrong ?

## Answer by oronimbus (score 3, accepted)

https://quant.stackexchange.com/a/71887

The displayed curve uses ACT/365 daycount with continuous compounding. The ZC is calculated by converting from simple discounting (ACT/360) to continuous compounding (ACT/365).

Hence, you can replicate the discount factor using the ZC rate displayed above:

`=EXP(-2.94084%*94/365)`

which gives 0.992455. As far as I remember this value is for display only and in the backend the curve will be stripped with the daycount that's applicable to your deal.

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.