How is a floorlet different from a caplet in terms of payoff and pricing?

Question

AcadiFi · Accepted Answer

A floorlet pays max(K - L, 0) x notional x tau at the end of the period, where L is the reference rate fixed at T. Economically, the floor buyer is protected if rates fall below K.

Black's floorlet formula mirrors the caplet but with a put:
Floorlet = notional x tau x DF(T+tau) x [K x N(-d2) - F x N(-d1)]
with d1 and d2 defined as in the caplet formula.

Example: Notional $15M, K=3.00%, F=2.60%, sigma=25%, T=2 years, tau=0.25, DF(2.25)=0.88.
d1 = [ln(0.026/0.030) + 0.5 x 0.0625 x 2] / (0.25 x 1.414) = (-0.1431 + 0.0625)/0.3536 = -0.228
d2 = d1 - 0.3536 = -0.581
N(-d1) = N(0.228) = 0.590
N(-d2) = N(0.581) = 0.719
Floorlet = 15,000,000 x 0.25 x 0.88 x [0.03 x 0.719 - 0.026 x 0.590]
= 3,300,000 x [0.02157 - 0.01534] = 3,300,000 x 0.00623 = $20,560

Put-call parity check: Caplet - Floorlet = tau x DF x (F - K) = 0.25 x 0.88 x (0.026 - 0.030) x 15M = -$13,200. So Caplet = Floorlet - 13,200 = $7,360.

Intuition: when forward is below strike, floorlet is in-the-money (has intrinsic value) and caplet is out-of-the-money.

How is a floorlet different from a caplet in terms of payoff and pricing?

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