Pricing Swaps with Separate Projection and Discount Curves
Summary
The document asks whether a curve built from three-month LIBOR swaps can price swaps with different floating-rate tenors or payment schedules. The response explains that post-crisis swap valuation generally separates projecting floating coupons from discounting cash flows: a three-month LIBOR curve supplies projected rates, while an overnight indexed swap curve is used for discounting when available.
A one-month LIBOR swap requires its own projection curve because the one-month and three-month rates contain a market basis; one tenor cannot simply be inferred from the other. The response attributes this distinction to differences in credit risk associated with the tenor of LIBOR payments and points to multiple-curve construction for further study. It offers a conceptual explanation rather than a worked valuation, and the quoted curve is illustrative. The precise curve setup depends on the market and available instruments.
Key ideas
- Swap valuation can use one curve to project floating coupons and another to discount cash flows.
- Three-month LIBOR coupons are projected from the corresponding tenor curve.
- One-month LIBOR swaps require a distinct projection curve when a tenor basis exists.
- A curve quoted for one swap tenor does not by itself price every other tenor or structure.
- The explanation is conceptual and gives no worked cash-flow valuation.
Tags
Full text
# Using a Swap curve to price Interest rate Swaps # Using a Swap curve to price Interest rate Swaps 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) - 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). ## Answer by BrownianBread (score 1) https://quant.stackexchange.com/a/66571 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.
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