Constructing Half-Year OIS Forward Rates from Swap Cash Flows

Summary

The question concerns how to derive a 1.5-year forward rate under OIS discounting when the available curve instruments have annual fixed payments and more frequent floating payments. It asks whether intermediate rates must be interpolated from full-year swap rates and what a 1.5-year swap rate represents.

The answer explains that payment schedules depend on the currency and contract conventions. In its example, the 1.5-year swap has fixed payments at six and eighteen months, alongside regular quarterly floating payments. Thus, a swap rate is tied to the actual cash-flow schedule; it is not inherently just an interpolation between annual rates. If the curve is calibrated only from one- and two-year swaps, however, the chosen interpolation method can materially affect intermediate rates. The answer recommends checking whether the resulting short-period forward rates look reasonable. It gives no equations or quantitative comparison, so it does not prescribe a specific interpolation scheme or fully address curve calibration.

Key ideas

• A swap rate reflects the fixed and floating payment schedules specified by the contract.
• A 1.5-year swap may include fixed payments at six and eighteen months, depending on conventions.
• Intermediate curve rates depend on the interpolation method when only annual swap quotes are available.
• Inspecting the implied short-period forward rates can help assess whether an interpolated curve is plausible.

Tags

# Dual discounted forward curve


# Dual discounted forward curve












I was wondering how to calculate the forward rates based on OIS discounting for the half year terms. I know how to do this for the full year terms -> just making sure that the two legs are equal to each other. The problem is that I don't have fixed payments on the half year terms. For example when one wants to calculate the 1,5 OIS discounted forward rate you only have 1 fixed payment versus 3 floating payments. How to deal with this? One method which can be used is just calculating the full year rates and then interpolate between these rates, but I wonder if there is a method which can calculate these rates without using interpolation?

Next to that what does a 1,5 swap rate exactly mean, is this just an interpolated rate because you will have the same problem here when there isn't a payment on the half years.

## Answer by Bozothegrey (score 3)

https://quant.stackexchange.com/a/28350

Which currency are you looking at ? Say that your 1y swap would have yearly fixed payments vs 3M floating payments. Your 1.5y swap would probably have:

- a fixed payment 6m after effective date and another fixed payment 18m after effective date

- regular quarterly floating payments

Your curve was built with 1y and 2y swaps, nothing in the middle ? Then yes, your interpolation choice would matter a lot. I would look at 3m forward rates and make sure that they optically make sense.

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