Caplet–Floorlet Parity and a Fixed-Pay FRA

Summary

The document shows how a long caplet and a short floorlet with the same strike can be combined to reproduce the payoff of a forward rate agreement in which the fixed rate is paid. The caplet payoff is the positive part of the reference rate minus the strike; the short floorlet contributes the negative of the positive part of the strike minus the reference rate.

For either rate outcome, adding those payoffs yields the reference rate minus the strike. This is a payoff-level explanation of put–call parity applied to interest-rate options, and it connects option positions to an FRA. The answer is concise and assumes both options share the same underlying rate and strike; it does not discuss discounting, settlement conventions, or other contract details that matter when comparing full market values.

Key ideas

• A long caplet pays the positive part of the reference rate minus the strike.
• A short floorlet pays the negative of the positive part of the strike minus the reference rate.
• Combining the two payoffs produces the reference rate minus the strike.
• The payoff identity corresponds to a fixed-pay FRA under matching contract assumptions.

Tags

# Answer by dm63 (score 1)


# Show that being Long a caplet & short floorlet (both with strike price K) is equivalent to a FRA where you pay the fixed rate K












How do you show that being long a caplet and short a floorlet (both with strike K) is equivalent to a Forward Rate Agreement where you pay the fixed rate K?

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/22351

yes it is put-call parity: long the caplet pays max(0; libor - K) short the floorlet pays -max(0; K-libor) add them up you always receive libor and pay K

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.