Say we have a 3-m LIBOR IRS (interest rate swap) with quarterly fixed payments (2 year contract), and we want to value this contract (after say 6 months has passed, i.e. there remain 1.5 years to maturity)

  1. We want to value the swap today (after 6 months has passed), using a Swap curve, i.e. the difference between the present value of the swap cashflows under the fixed leg as agreed at initiation, and then the 1.5 current market swap rate.

If a Swap curve is constructed with reference to e.g. a 3-month LIBOR Interest rate swaps and with the fixed payments also 'quarterly. i.e. you basically have 3-m Libor Swap curve (as example below).

Current 19 Aug

1 Year 0.131%

2 Year 0.273%

3 Year 0.463%
5 Year 0.753%

7 Year 0.943%
10 Year 1.128%
15 Year 1.309%

30 Year 1.433%

Can this Swap curve (with tenor 1y to 30y) be used to value ONLY a similar IRS contract, i.e. 3m LIBOR Swap with quarterly fixed payments, or can this curve be used to value other swap contracts as well (1m libor vs monthly fixed).


1 Answer 1


You will need to do some reading around multiple curve construction, as to price a IRS on 3M Libor you need more than just the 3M Libor curve in any case. Coupons are computed using a projected 3M rate from the 3M Libor curve, but the cashflows in both the fixed and floating leg are discounted at the OIS rate (if it exists for the economy).

To price a 1M Libor IRS you will need the 1M Libor curve which is not the same as taking the 1M forward from the 3M Libor curve due to the non-zero 1M-3M Libor basis in the market, in fact you use these instruments to find the 1M curve from the 3M + OIS. The rationale behind this is from a credit risk perspective around the time of the 2008 financial markets crash, a series of three 1M Libor payments is deemed less risky than one 3M coupon, hence the 3M coupon typically carries a higher forward rate.

Please see Introduction to Multiple Curve construction and the references contained therein for an introduction to the subject.

  • $\begingroup$ Thank you @BrownianBread. I've seen that instead of using OIS to discount the cashflows, the swap rate at the time of evaluation is used to calculate the various discount factors, in this example the 1.5 year swap rate will be used. On page 14 of this article.: treasurer.ca.gov/cdiac/publications/math.pdf. Is this incorrect? $\endgroup$
    – Student
    Aug 23, 2021 at 9:19
  • $\begingroup$ This is pre-2008, so using the old "single curve" methodology, look for refs from 2010+. I would focus on using an OIS curve + Libor tenor curves to price derivatives to understand the general case and then you can simplify to discount curve = projection curve where appropriate. The choice of the discounting curve is a whole topic in itself, it is usually a spread over OIS as the risk free rate that you discount at should reflect your institutions ability to collateralise the trade. See eusp.org/sites/default/files/archive/ec_dep/Lecture_Posters/… for example. $\endgroup$ Aug 23, 2021 at 9:41
  • $\begingroup$ Thank you @ Brownianbread, I have 3 extra questions if you would be able to answer. 1. can one find/derive the 3-month LIBOR forward curve from a 3m LIBOR SWAP curve (i.e. is there a direct formula/relationship)? or is this either not possible or too complex. and secondly. 2. IS there currently ONE correct/standard way/method to value an IRS, e.g. whether using a Forward curve and Discount rate method OR using the discount and swap curve method? (3. and is the assumption that all users will price/value swaps using multi curves, or will some still use a single curve methodology?) $\endgroup$
    – Student
    Aug 23, 2021 at 10:39
  • $\begingroup$ 1. You need to bootstrap the 3M Libor curve from the instruments you find in the market, such as the ones listed in the original post. Once bootstrapped you can use the forward rate formula on the "3M Libor discount curve" to get the appropriate forward rates. en.wikipedia.org/wiki/Bootstrapping_(finance). 2. This becomes a complex question when accounting for collateral agreements between counterparties and the jurisdictions each party is in, but in general the accepted method is to use multicurve. 3. A general rule is if the OIS market exists for that currency then multicurve. $\endgroup$ Aug 23, 2021 at 13:54
  • $\begingroup$ I am not sure what you mean by your answer to my first question. I don't see how you mentioned getting to the swap curve by using bootstrapping? I understand bootstrapping as the process of obtaining the spot curve (Libor zero curve), from using zero-coupon bonds. and yes, once this zero curve has been constructed the forward rates can be obtained via the formula. But not sure how this links to getting the swap curve? (or getting the swap curve from the forward curve)? @BrownianBread $\endgroup$
    – Student
    Aug 23, 2021 at 19:14

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