Choosing Discount Curves for Cash Flows and Understanding OIS

Summary

The document explains that discounting should reflect the characteristics and financing context of the cash flow. It gives government bond investments as an example for which a Treasury yield curve may be appropriate, and a company’s project cash flows as a case where a curve reflecting its borrowing conditions or sector could be relevant. Where an ideal curve is unavailable, the answer suggests using a comparable proxy. It also describes bootstrapping as a common way to construct yield curves.

The response defines an Overnight Index Swap as an agreement exchanging a fixed rate for a floating rate linked to an overnight index and compounded over a term. This helps explain why OIS curves enter discounting discussions, but the source does not develop the modern details of collateralized derivatives valuation or distinguish discounting from forwarding curves. Its examples are illustrative, not a comprehensive rule for selecting curves across bonds, swaps, and other instruments; curve choice depends on the cash flow and valuation framework.

Key ideas

• Discount cash flows using a curve suited to their issuer, instrument, and financing context.
• A comparable sector or market curve may serve as a proxy when an ideal curve is unavailable.
• Bootstrapping is identified as a common method for constructing yield curves.
• An OIS exchanges a fixed rate for a floating overnight-index rate compounded over a term.
• The examples do not provide a complete framework for modern multi-curve valuation.

Tags

# When to use what discount rate?


# 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?

## Answer by python_enthusiast (score 3)

https://quant.stackexchange.com/a/35632

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.

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.