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Using Actual Day Counts to Reproduce Zero-Curve Discount Factors

Article Quant Q&A · Author: PalimPalim
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Summary

The document investigates a mismatch between a discount factor calculated from a quoted zero rate and a displayed Bloomberg value. It compares two compounding conventions: periodic compounding and simple interest. Neither reproduces the displayed factor when the calculation uses a 90-day interval, though simple interest comes closer.

Changing the interval to 91 days under simple-interest discounting produces a matching result. The explanation is that the relevant dates are September 3 and December 3, which are 91 days apart. The example shows why reproducing zero rates or discount factors requires using the actual date interval as well as the appropriate compounding convention. It is a single date-specific explanation, however, and does not establish which day-count or compounding conventions apply to other instruments, curves, or Bloomberg settings.

Key ideas

  • A discount factor depends on both the quoted zero rate and the time interval used.
  • Different compounding conventions can produce different discount factors.
  • The example’s relevant dates are 91 days apart, explaining the discrepancy from a 90-day calculation.
  • A matching result in this example does not determine conventions for other instruments or curve settings.

Tags

Fixed incomeDerivatives pricingStatistics
Full text
# discount factor, zero rates, zero curve from BBG


# discount factor, zero rates, zero curve from BBG












How can I calculate the discount factor for row 1?

I would do

$$ \frac{1}{(1+ 2.13763/100)^{(90/360)}} = 0.994726197703956 $$

My ultimate goal is to reproduce the Zero Rates. Any hints welcome. but this does not agree with the screenshot ($0.994626$).

Update

According to here I might need a different form of compounding. Still the results do not match. $$ \frac{1}{1+ (2.13763/100)*{(90/360)}} = 0.994684332326721 $$

This is closer, but far from an exact match.

Using 91 instead of 90 and second version, I do get a matching result.

$$ \frac{1}{1+ (2.13763/100)*{(91/360)}} = 0.994625586781402 $$

Why would I be using 91 days instead of 90?

## Answer by PBD10017 (score 0, accepted)

https://quant.stackexchange.com/a/53256

Because there is 91 days between 2019-12-03 and 2019-09-03.

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.