Discount Curve built-up

Question

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 1

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.