Dual-Curve Calibration with Interest-Rate Basis Swaps

Summary

The response explains how basis swaps help build a consistent family of interest-rate curves when liquid instruments provide direct market quotes for only some tenors or reference rates. It describes a typical set that can include overnight-indexed discounting and several interbank offered-rate curves, such as one-month, three-month, and six-month curves.

Rather than calibrating every curve from bespoke instruments, practitioners anchor the construction to liquid market instruments, for example short-dated futures and longer-dated swaps. Basis swaps linking different floating-rate indices or an index to overnight rates then provide relative pricing information to infer the other curves. The aim is for the resulting curve set to reproduce prices of commonly quoted instruments consistently. The answer is a high-level concept sketch: it does not explain the calibration equations, conventions, discounting setup, or numerical implementation, and the specific curve tenors and instruments vary by market.

Key ideas

• Interest-rate valuation may require separate overnight and interbank-rate curves.
• Liquid futures and swaps provide direct calibration points for some parts of the curve set.
• Basis swaps relate curves tied to different floating-rate indices or to overnight rates.
• Dual-curve construction seeks a curve set consistent with prices of quoted market instruments.

Tags

# Basis Swap Dual Curve Calibration


# Basis Swap Dual Curve Calibration












The long end of the Libor swap curve needs to be constructed from Basis Swaps because there are no other instruments traded. Can please someone explain the concept of Dual Curve Calibration?

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/50392

Actually it is not just the long end of the swap curve it is any part of the curve that needs some form of basis swaps to be calibrated.

A set of curves in any currency usually encompasses the following: { OIS curve, 1M IBOR curve, 3M Ibor curve, 6M Ibor curve } at a minimum.

It is not practical for interbank markets to trade completely bespoke products so the liquid points might be for example: 3M interest rate futures in the first 3Y, then 6M IBOR swaps from 3Y to 50Y at regular intervals.

In order to construct other curves you need to base them reletive to these liquid instruments, so you often have, for example a 6m/3m basis swaps, and 3m/ois basis swaps which allows you narrow down the curves in different sections relative to each other and end up with a consistent set of prices that agree with the normally quoted interbank products.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.