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USD Discount Curves: OIS Discounting and Separate LIBOR Projection

Article Quant Q&A · Author: athos
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Summary

The document explains the shift from single-curve swap valuation to multi-curve valuation. Before the financial crisis, practitioners commonly treated LIBOR as a risk-free rate and used it to construct swap curves. Under modern collateralized valuation, an OIS-based curve is generally used to discount cash flows, while a separate three-month LIBOR curve projects the floating cash flows tied to that tenor.

This distinction means projection and discounting require different curves: LIBOR forwards estimate the floating payments, and OIS discount factors convert those payments to present values. The response notes that the precise discounting curve depends on the collateral terms. It does not provide the requested market-data command or a step-by-step curve-building recipe, and its description is limited to the stated collateralized setting.

Key ideas

  • A three-month LIBOR curve can project floating payments linked to that tenor.
  • For collateralized trades, OIS discount factors are generally used to value future cash flows.
  • Modern swap valuation may require separate projection and discount curves.
  • The appropriate discounting setup depends on the collateral agreement.

Tags

Fixed incomeDerivatives pricingStatistics
Full text
# Discount Curve built-up


# Discount Curve built-up












For a particular currency, let's say for USD, I'd like to know how to construct a discount curve?

I've an impression that one professor told me that for USD, less than 3 months, it's using Libor curve; more than 3 months, up to 3 years, it's using ED future rate; then afterwards it's using IRS rate.

Then I come to this paper from John Hull talking about using OIS rates if the portfolio is collateralized, while LIBOR rate shall be used if not.

In the end I'm a bit lost.

If a few mores could be said on how (e.g. which Bloomberg command) to retrieve the discount curve of USD, that's even better.

## Answer by Helin (score 1, accepted)

https://quant.stackexchange.com/a/17491

Before the financial crisis, we used to assume that LIBOR is a risk-free rate and built swap curves in pretty much the same way your professor taught.

Nowadays, OIS discounting is the norm (actually depends on the exact collaterialization mechanism, but let's not go there...). Simply put, you need to have a 3-month LIBOR curve to project 3-month LIBOR forwards and the corresponding floating cash flows. However, the cash flows are not discounted using LIBOR discount factors to produce the present values. Instead a separate discount curve based on OIS should be used. So the swap curve is really a package of curves ("multi-curve"). OpenGamma has published a good documentation Multiple Curve Construction that describes the methodology.

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.