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Swaption Carry Includes Curve and Volatility Rolldown

Article Quant Q&A · Author: Jonny
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Summary

The document considers how to define carry for a USD payer swaption with a six-month expiry and a ten-year underlying swap. It questions a simple calculation based on subtracting a short-term LIBOR fixing from a ten-year yield, and whether that spread alone represents the position’s carry.

The response says the term is not necessarily well-defined for this option and suggests examining two sources of change as time passes: the swap rate’s movement along the yield curve and the option’s movement along the implied volatility term structure. For example, one could compare the forward-starting swap rate and volatility associated with the option’s remaining life to those at a later date. The document gives a conceptual distinction, not a complete valuation or carry formula. It does not specify conventions, discounting, volatility surface dynamics, or the position’s hedges, all of which affect a practical carry estimate.

Key ideas

  • A single spread between a long-term yield and a short-term rate may not capture swaption carry.
  • Rate carry can include the change in the relevant forward swap rate as the option approaches expiry.
  • Volatility carry can include movement along the implied volatility term structure.
  • The appropriate carry measure depends on the instrument and its market conventions.

Tags

OptionsFixed incomeCarryVolatility
Full text
# Carry on a USD 6m10y payer swaption


# Carry on a USD 6m10y payer swaption












Trying to calcuate the carry on a 6m10y payer swaption.

So far, I have used: carry = spot rate - libor

Do I use the 6m LIBOR rate (0.15213%)? And do I just use the 10y yield for the spot rate (1.26)?

So is the carry 1.11?

Any help would be much appreciated.

## Answer by user42108 (score 1)

https://quant.stackexchange.com/a/66108

Not sure that carry is well-defined in this case, but in general I'd say you want to consider both rates "carry" (i.e. rolldown on the yield curve between 6mf10y and 3mf10y for e.g.) and vol "carry" (i.e. rolldown on the vol term structure between 6m vol and 3m, for e.g.).

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.