# When to use what discount rate?

By discount curve $D(t)$ I mean the discount rate applied to a cash payment or receipt at time $t$.

What is the correct terminology to use? I have seen the term "yield curve" thrown around, but I'm not exactly sure what it typically means, given that there are different compounding conventions, definitions of yield, etc.

Is the same discount curve used for everything? In other words, are cash flows from government bonds, corporate bonds, swaps, etc. all discounted using the same discount curve? How is this discount curve typically constructed and where does OIS come into the picture?

• "risk free discount curve" is correct terminology, sometimes called "risk free zero coupon yield curve". As you point out "risk free yield curve" is slightly ambiguous (there are different kinds of y.c.) but OK. The curve is found by "fitting" or "bootstrapping" observed yields of risk free securities, such as US Treasuries and (at the short end) OIS. You use the curve to discount any risk free payment i.e. any payment sure to occur. – Alex C Aug 12 '17 at 22:59

Ideally, you would discount a certain cash flow by its appropriate curve.

For example:

1) you would discount the cash flow of your fixed income investments by the yield curve of the Treasury market;

1) you would discount the cash flow of an oil company by the interest curve that the it encounters when financing its ventures. If such a ('ideal') curve is not available, you might use the equivalent one from the oil sector, etc.

The yield curves are typically constructed using bootstrap: Wikipedia link to Bootstrapping

OIS means Overnight Index Swap. As a swap, the two parties involved agree to exchange cash flows (notional amount): one is the interest accrued by using a floating rate and the other using a fixed rate. As it is overnight, rate swap whose floating leg is tied to an overnight rate, compounded over a specified term.