Bootstrapping a Swap Zero Curve Between Floating-Rate Reset Dates

Summary

The document asks how to bootstrap a zero curve from swap quotes when valuation occurs between floating-leg reset dates. It explains why the usual par-at-reset assumption does not directly apply: the floating leg may not be worth par, and the swap may have begun earlier, so its value need not be zero. The example considers a short-dated USD interest-rate swap with semiannual floating payments and raises the related problem of valuing the existing contract.

No solution, derivation, or numerical evidence is provided; the text is a request for guidance. It identifies important modeling questions, including how to account for accrued interest and the next floating payment, and how differing leg frequencies affect curve construction. Its scope is therefore diagnostic rather than instructional, and it does not establish a specific bootstrapping convention or address details such as collateral, discounting curves, or market conventions.

Key ideas

• A floating-rate leg is not necessarily valued at par between reset dates.
• A swap that is already in progress may have a nonzero market value.
• Bootstrapping from swap quotes requires accounting for the timing of the next floating reset and payment.
• The document raises, but does not solve, curve construction when fixed and floating payment frequencies differ.

Tags

# How to bootstrap zero curve using swap curve when Today's are not reset date?


# How to bootstrap zero curve using swap curve when Today's are not reset date?












I know how to build Zero Curve using Swap Curve when today's are reset date. Because, In the reset date, Floating rate bond's value is exactly par value. So we can make equation with Fixed rate bond!

However, the problem is when it is not reset date.

Let's look at the problem with quote

Above picture is arbitrary sample of USDIRS Quote. Let's assume Floating leg frequency is 6 Month.

Then Now I start with "1 Day" swap rate '0.01576' to bootstrap with swap rate.

Now! the Floating leg's payment is (1 + r/2)*FaceValue "1 day after!" Also the Fixed leg's payment is (1 + swaprate/2)*FaceValue "1 day after!"

But I assumed today is not reset date. So I cannot make equation because of those reasons.

- Floating Leg is not Par Value because it's not reset date today.

- Because it's not reset date, it is also not contract date. That means, the contract value is not 'Zero'

So Considering just only this Swap Rate Quote table, except using market Spot curve How can I make Spot curve and bootstrap to make implied spot(Zero) curve? and How can I value this Swap Contract?

Is there any reference that explain extract implied spot curve when it is not reset date or the leg's frequency are different each other?

It really gets me in trouble. Please help me

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.