Caplets as Calls on Forward Interest Rates

Summary

The document explains why a caplet is described as a call option. Its payoff is positive when the reference interest rate for a calculation period exceeds a contractually specified strike, making the payoff analogous to a call’s positive-part payoff. The underlying is the relevant forward interest rate, such as LIBOR, rather than necessarily a stock or another conventional security.

It also distinguishes the payoff description from practical volatility modeling. Market quotes are often available for a strip of caps, so a bootstrapping procedure is used to infer the volatility of individual caplets. The discussion is conceptual and does not provide pricing formulas, settlement conventions, or a numerical example. The precise payoff and valuation depend on contract details, including rate definitions and accrual periods, so the analogy alone is not a complete pricing model.

Key ideas

• A caplet pays when its reference rate exceeds the agreed strike.
• The caplet payoff has the positive-part form associated with a call option.
• The underlying of a caplet is a forward interest rate rather than necessarily a stock.
• Individual caplet volatilities may be inferred by bootstrapping from cap volatility quotes.
• Contract conventions are needed for a complete payoff and valuation specification.

Tags

# difference between caplet and call


# difference between caplet and call












I wanted to know the difference between a caplet and a call. In my course (Interest rate models and curves) , we said that a caplet is a call option. Is it really true? Thanks

## Answer by Gordon (score 2, accepted)

https://quant.stackexchange.com/a/21604

A caplet is a call, as the payoff is given by $(L-K)^+$, where $L$ is the libor rate for a given calculation period and $K$ is the pre-agreed rate. However, in practice, the volatilities for a strip of caps are usually provided, and then a bootstrapping algorithm is needed to back out the volatility for each caplet.

## Answer by SmallChess (score 1)

https://quant.stackexchange.com/a/21607

Call option gives the exercise strategy, but it doesn't actually tell you anything about the underlying. It could be a stock, a LIBOR interest rate, a bond or any tradable asset.

The simplest call option would be an equity call option, where the underlying is a stock. In a caplet, the underlying is the forward interest rate (eg: LIBOR), you would exercise a caplet if the interest rate at maturity is more than than the rate specified in the option contract.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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