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
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.
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.