The swap rate for a relevant maturity on the assumption of a generic structure for the underlying swap transaction. In other words, it the par-swap rate that is applied to a given swap tenor. The CMS rate is typically calculated off the zero swap curve with convexity adjustment. In terms of composition, the CMS rate is equal to the swap rate in addition to an extra term function of the covariance under the annuity measure between the forward swap rate and the forward annuity. Therefore, the CMS rate depends on the following three factors:
- The yield curve by way of the swap rate and the annuity.
- The volatility of the forward annuity and the forward swap rate.
- The correlation between the forward annuity and the forward swap rate.
The CMS rate is usually observed on a daily, weekly or monthly basis within the coupon period.
A CMS swap, for example, is the periodic exchange of a CMS rate for either a fixed rate or a floating rate (typically LIBOR). Such as swap may involve the exchange of a USD 2-year CMS/10-year CMS for LIBOR. It consists of a standard quarterly, ACT/360 floating leg based on 3-month LIBOR versus the quarterly fixing and payment (accrued 30/360) of a 10-year par-swap rate on the CMS leg, with both legs spanning 2 years.
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