Bootstrapping Long-Term Swap Discount Factors from Market Swap Rates

Summary

The document asks how to price a long-maturity fixed-for-floating interest rate swap when the available LIBOR curve quotes extend only to short maturities. Its answer is to use quoted market swap rates beyond the end of the Eurodollar futures strip, described as the more liquid source of long-term information about future LIBOR rates. These swap quotes provide constraints for extending the curve.

The curve construction involves solving for the forward LIBOR rates implied by the observed swap rates, a process commonly described as bootstrapping and often handled as a global curve-solving problem. Once the curve is constructed, its discount factors can be used to value the fixed cash flows and determine the par swap rate. The response gives no equations, instrument conventions, numerical example, or treatment of collateral and modern multi-curve discounting. Its explanation is framed around LIBOR-era conventions and should not be read as a complete current-market curve construction recipe.

Key ideas

• Short-maturity LIBOR quotes alone do not provide the inputs for a long-dated swap valuation.
• Market swap rates can constrain the curve beyond the Eurodollar futures strip.
• Curve construction solves for forward LIBOR rates implied by quoted swap rates.
• The response gives a high-level description without detailed conventions or a worked calculation.

Tags

# Constructing Swap Curve from LIBOR


# Constructing Swap Curve from LIBOR












Say I'm considering a long maturity fixed rate swap, for instance 20 years paid semi annually. Now I want to find the fixed rate for this hypothetical swap. I understand that this fixed rate is going to be predicated on discount rates based on the current term structure of the LIBOR yield curve (or whatever reference rate).

Because of the very long maturity of the swap, however, I'll need to have LIBOR discount rates for payments that will be made very far in the future. Now it may be the case that LIBOR rates are only quoted up to 1 year.

So I need the discount rate for the final payment at the end of the swap, in the distant future, to compute the swap fixed rate. However I don't have a LIBOR discount rate for that payment because it isn't quoted up to that maturity.

To compute the swap fixed rate, how do I find the appropriate discount factors beyond what's quoted in the LIBOR curve?

## Answer by atkins (score 1)

https://quant.stackexchange.com/a/29818

You use quoted market swap rates. Once you reach the end of the Eurodollar strip, about 3 years out, swaps are the most liquid source of information about expected future Libor rates. Since swap rates are essentially long-term averages of Libor rates, you have to solve for the implied forward Libor rates (sometimes called "bootstrapping the yield curve", but more commonly now it's a global solving problem).

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.