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How OIS Curves Are Built and Used for Discounting

Article Quant Q&A · Author: Bogaso
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Summary

An overnight index swap curve is a term structure built from market instruments referencing an overnight rate. The answer explains that curve construction uses instruments such as futures and swaps across maturities to infer discount factors and forward rates; it is therefore more than a list of quoted swap rates. Futures may require a convexity adjustment because their payoff structure differs from swaps. Conventions such as payment frequency and day count depend on the currency and instrument; the response gives examples for SOFR and €STR swaps.

The curve is used to discount collateralized cash flows, and may be constructed before a separate forwarding curve in a multi-curve framework. For example, OIS discount factors can value the known fixed leg of a Libor swap while the unknown forwarding curve is solved so both legs have equal present value. Market practice has shifted toward relevant risk-free overnight rates for discounting, but the answer’s transition dates and instrument conventions reflect its historical context and should not be treated as current market guidance.

Key ideas

  • An OIS curve is bootstrapped from instruments at different maturities to infer discount factors and forward rates.
  • Quoted OIS swap rates are inputs to curve construction rather than the entire curve representation.
  • Futures may need convexity adjustments when used alongside swaps to build a curve.
  • OIS discounting and a separate forwarding curve can coexist in multi-curve valuation.
  • Payment and day-count conventions vary by market and instrument.

Tags

Fixed incomeDerivatives pricingFuturesStatistics
Full text
# What is Overnight index swaps (OIS) curve


# What is Overnight index swaps (OIS) curve












Overnight index swaps (OIS) curves became the market standard for discounting collateralised cashflows.

However I failed to understand what is the meaning of the `Curve` here? My assertion is : It is basically discount rates for different maturities which were derived from Overnight index swaps with different maturities.

Is my assertion correct? If it is indeed correct then what is the compounding frequency for those discount rates? Is that annual? Day count convention? Is it Actual/360?

Or, it is just the Swap rates for most-liquid Overnight index swaps of different maturities?

Can you please provide some snapshot how the OIS-Curve actually looks like?

## Answer by AKdemy (score 3, accepted)

https://quant.stackexchange.com/a/63748

OIS is overnight index swap: fixed float swap with floating rate based on some overnight rate

Traditionally (some examples):

- EONIA (EUR)

- Fed Funds (USD)

RFR: New Risk free rates (secured overnight funding rate):

- ESTA (EUR)

- SOFR (USD)

In terms of what these curves look like: Reference is the underlying OIS. The curve uses instruments (Futures, Swaps) to construct (strip) discount factors and forward rates implied by those instruments. For example, a SOFR swaps curve will reference SOFR rate and use SOFR futures (not necessarily but possible, requires convexity adjustment though as future is linear in rates as opposed to convex FRA or swaps) and SOFR OIS swaps for varying maturities. These swaps for example are fixed - float with fixed leg typically having annual pay frequency and ACT/360 daycount. The float leg has daily reset frequency, annual pay frequency and ACT/360 daycount. ESTR is the same but usually using a basis spread to Euribor for longer tenors (at the moment) due to liquidity and market practice.

What you refer to is the current dual curve stripping framework. For example, swaption vol is now quoted with SOFR discounting, CME and LCH moved to SOFR PAI and discounting on Oct. 16 2020 on new AND legacy swaps.

For EUR cleared, major CCPs did this since July 27 2020.

The market switched to discounting with the relevant RFR rates on the dates above. Hence, if you have a dual stripped curve (e.g. 3m US libor), you use SOFR and no longer OIS (FF).

This really means that you discount the cashflows with OIS. Frequently, the OIS curve (SOFR for example) is stripped prior to Libor curve for example. So you find the present value of the fixed and float leg of a Libor swap, using OIS as discount factor. Thus, the only unknown values are the payments of the floating leg (PV fixed is already known). The exercise is to find discount factors of the floating leg that make both PVs equal.

It is not just discounting though (at least not looking forward). ISDA fallbacks will apply from 31 December 2021 for GBP, JPY, CHF and Euro-LIBOR and from 30 June 2023 for USD LIBOR. Even if there were some synthetic or "zombie" Libor after it officially ceases to exist, it is expected that liquidity will drop significantly. Note that the FED have issued supervisory guidance encouraging banks to “cease entering into new contracts that use USD LIBOR as a reference rate as soon as practicable and in any event by December 31, 2021”.

Once Libor is gone, your major reference will be RFR throughout.

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.