Swap Curve Construction and Cash Flow Dates Beyond One Year
Summary
The document asks why a market-convention one-year interest rate swap can involve a final payment date slightly beyond one year from the trade date. The example uses a two-day spot lag and quarterly floating accruals; adjusted dates put the final cash flow beyond the anniversary. For valuation, the cash flow is discounted at its actual payment date, while its year fraction depends on the chosen day-count convention, commonly Actual/365 in the discussion.
The answers distinguish a par swap rate from a zero rate and note that curve construction and interpolation affect how rate instruments map to zero-curve points. Localized dependence on nearby curve points is desirable, but maintaining smoothness or shape properties can create spillover. The discussion gives convention and interpolation explanations rather than a full calibration procedure. The exact dependence therefore depends on instrument conventions and the curve model; the example does not imply that every one-year swap uses the same dates or has identical sensitivity beyond one year.
Key ideas
- A swap's maturity label follows market conventions and need not match an exact year fraction from trade date.
- Discount each cash flow at its actual payment date, with the curve's day-count convention determining its time coordinate.
- A one-year par swap rate is distinct from a one-year zero rate and can have exposure to longer curve instruments.
- Curve interpolation can spread an instrument's sensitivity beyond its nominal maturity.
- Curve-building results depend on conventions, instruments, and interpolation choices.
Tags
Full text
# Does a 1Y swap depend on zero curve beyond the 1Y point?
# Does a 1Y swap depend on zero curve beyond the 1Y point?
When using market swap rates to calibrate a discount curve, it seems that the PV of a 1Y swap depends on the zero curve at points beyond the 1Y mark.
For example, a USD 1Y swap with trade date today (Wed 16th March 2016) and a spot lag of 2 days will have an effective date of Fri 18th March 2016, and the floating leg accrual periods (after adjusting using modified following convention) are
```
Period Start Date End Date
---------------------------------
1 18-Mar-2016 20-Jun-2016
2 20-Jun-2016 19-Sep-2016
3 19-Sep-2016 19-Dec-2016
4 19-Dec-2016 20-Mar-2017
```
The final payment clearly depends on today's LIBOR curve for 20th March 2017, which is more than one year after today (in fact it is 1.011 years in ACT/365 day count).
It seems odd to me that the PV of a 1Y swap would depend on points on the zero curve beyond the one year mark, but that seems to be the case if you correctly compute the start and end dates.
Is it the case? If not, how do institutions normally deal with this?
## Answer by Helin (score 2, accepted)
https://quant.stackexchange.com/a/24917
The problem is that the definition of "one year" depends on the market convention:
For pricing, what you need is a unique discount factor for each date. It shouldn't matter how you define "year" internally within your model. In other words, the final cash flow should be discounted with $d(\text{3/20/2017})$. How you convert that 3/20/2017 into a year fraction is entire up to you. In a discount curve setting, Actual/365 is the most prevalent choice.
## Answer by dm63 (score 1)
https://quant.stackexchange.com/a/24919
This all depends how you build the swap curve. If you are using just annual zero rates to build the curve, the answer may be that a one year par rate (paid quarterly or semi annually) is not the same as a one year zero rate. Specifically, it has slightly shorter duration. Therefore the hedge for a one year par rate, in terms of zero rates, should contain a small amount of 2 year swaps (and possibly longer swaps) in the opposite direction to the one year swap. There's nothing wrong with that.
Dealers don't use zero swaps to build curves. They use eurodollar futures and par swap rates to build curves, then imply the zero swaps, just fyi.
## Answer by achirikhin (score 1)
https://quant.stackexchange.com/a/79323
Depends mostly on the curve interpolation method, not on the instruments you build it from. It is a desired property that dependency is localized (this is the jargon for what you describe), but for the curve to be smooth, monotone and/or convex, one may have to accept some spillover.
Google "convex monotone" or search for other works on the curve interpolation, to which Pat Hagan has contributed.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.