What makes a Constant Maturity Swap different from a vanilla swap?

Question

AcadiFi · Accepted Answer

A Constant Maturity Swap pays one leg tied to a long-term swap rate that is reset periodically, such as the 10-year swap rate reset every quarter. The counter leg pays a short-term reference like 3-month SOFR, possibly plus or minus a spread. CMS effectively lets you take a view on the slope of the yield curve without rolling positions manually.

Suppose Aurora Insurance wants exposure to the 10-year swap rate to match long-duration liabilities but does not want to buy a new 10-year swap every quarter. They enter a 5-year CMS receiving the 10Y swap rate quarterly and paying 3M SOFR flat. Each quarter, the 10Y rate is observed; the difference versus SOFR is settled on a notional.

Pricing requires a convexity adjustment because the observed swap rate enters the payoff linearly but the natural martingale measure is for the annuity-weighted swap rate. The adjustment uses the swaption volatility surface. For a 10Y CMS rate with σ = 0.85%, paid 0.25 years forward: adjustment = 0.5 × σ² × T² where T ≈ duration of the 10Y swap (about 7.9). Result: ~26 bp added to the forward.

CMS caps and floors extend this further, paying max(CMS rate minus strike, 0). They are popular with pension funds hedging long-dated cost-of-living adjustments.

What makes a Constant Maturity Swap different from a vanilla swap?

Master Level II with our CFA Course

Related Questions

Practice Questions