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Constant Maturity Option


A cap or floor whose underlying variable is long-term government (CMT) or swap rates (CMS), whose day count and frequency of payoff are similar to those of a short-term rate. For example, a 5-year quarterly option on a 10-year rate struck at 7% would pay (if a cap) the difference between the 10-year rate and the strike every quarter for the next ten years, or zero, whichever is greater. Likewise, a 5-year quarterly option on a 10-year rate struck at 5% would pay (if a floor) the difference between strike level and the 10-year rate every quarter for the next ten years, or zero, whichever is smaller.

The day-count used for the payoff calculations corresponds to that of a given quarter. In analogy to a vanilla cap/ floor, the payoff is made in arrears. The only difference between a vanilla option and a constant maturity (CMS) option is that, instead of comparing LIBOR to the strike, the 10-year swap rate is compared to the strike. This option can be seen as a basket of swaptions on a swap rate of fixed tenor (say, 10 years) structured like a LIBOR cap or floor.



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Derivatives have increasingly become very important tools in finance over the last three decades. Many different types of derivatives are now traded actively on ...
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