Converting Short-End OIS Par Rates into Zero Rates

Summary

The document addresses how to obtain an initial short-maturity zero-curve point from a tradable overnight index swap quote. Its answer focuses on day-count conventions: quoted OIS par rates may use an ACT/360 basis, while the zero rates delivered to users may be expressed using ACT/ACT or another chosen convention. Treating the two rates as directly interchangeable without accounting for their accrual bases can therefore produce a mismatch.

The suggested process is to use the midpoint of the bid and ask quote to infer the discount factor under the quote’s day-count basis, then express that same discount factor as a zero rate under the desired basis. The response characterizes the zero rate as the par rate adjusted for the chosen day count. This is a compact explanation for the short end and does not spell out calendar, payment-date, compounding, or instrument-specific conventions. Those details matter in a production curve build, and the document does not discuss later curve points or broader bootstrapping steps.

Key ideas

• OIS par quotes and zero rates can use different day-count conventions.
• Infer a discount factor from the quoted swap rate using the quote’s accrual basis.
• Convert that discount factor into a zero rate under the day-count convention desired for the curve.
• The short explanation leaves calendar, payment-date, and compounding details unspecified.

Tags

# Starting short-end OIS zero curve building


# Starting short-end OIS zero curve building












I understand the concept of bootstrapping and building the curve when we have the values for first few maturities. However, I can't quite get how the initial values for zero curve rates are derived from tradable instruments. As I understand, these values are directly implied from OIS par rates.

Can someone please clarify, how, given, say a 1M OIS swap bid and ask, can I get the zero curve point at 1M maturity?

## Answer by sashkello (score 2)

https://quant.stackexchange.com/a/28417

I think I figured it out. The problem was with day count conventions.

OIS par rate bid/ask are quoted in 360/ACT form, while zero curve rates are universalized to ACT/ACT (or whatever else is desired by the end user). Therefore, to get the zero rates, mid price of OIS swap is used to find the discount factor as 1/(1+r)^t(360/ACT) from which then zero rate r0 can be backed out 1/(1+r0)^t(ACT/ACT). So, they are essentially same thing, with a desired day count adjustment.

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.