Caps, Floors, and Caplets: Market Structure, Payoffs, and Black's Formula

A floating-rate borrower who pays six-month LIBOR on a loan is exposed to rate increases. An interest-rate cap is an insurance contract that caps the effective rate paid: if LIBOR exceeds a strike $K$ at any reset date, the cap seller pays the difference to the buyer. In practice, a cap decomposes into a strip of caplets — one option per reset period — each of which prices independently via Black's formula under the $T_k$-forward measure. This market structure makes caps among the most liquid rate derivatives: a single traded cap price implies a full term structure of single-period optionality. The symmetric floor and its parity with the cap against a fixed-rate swap are the calibration anchors for every interest-rate model.