Interpolating Discount Factors for Non-Standard Swap Maturities

Summary

The document asks how to obtain discount factors for payment dates that do not align with standard swap payment schedules, using a forward starting long-dated interest rate swap as an example. Such cash flows may fall between dates supported by a bootstrapped curve, creating a need to estimate discount factors at non-standard maturities when calculating a par swap rate.

The response says that interpolation is the practical approach and that market participants generally do not disagree much over an example of this kind. It does not specify which interpolation variable or method to use, explain curve-construction conventions, or establish a formal universal procedure. The note therefore conveys the basic market practice while leaving implementation choices and instrument-specific conventions open.

Key ideas

• Non-standard swap payment dates require discount factors between standard curve maturities.
• Interpolation is used in practice to estimate discount factors for those dates.
• The response suggests market participants generally agree on such estimates in the example discussed.
• The document does not prescribe an interpolation method or curve-building convention.

Tags

# Determining discount factors for non-standard maturities


# Determining discount factors for non-standard maturities












Let's say we'd like to find a par rate for a 1 month forward starting 20-year interest rate swap. In this case, we'd need to discount cash flows for the payment periods shifted +1 month from standard semiannual or quarterly payments (which we can find by bootstrapping from frequent 1st year values and yearly rates). And annual rates should available well past the final date.

Is there some standard approach to find these discount factors? I assume since par rate is something which defines swaptions' fixing values (its strike), it should be some agreed procedure and not just interpolation.

## Answer by dm63 (score 1, accepted)

https://quant.stackexchange.com/a/28312

No it's just interpolation. In practice there isn't much disagreement among participants for something like one month 20yr forward rate.

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.