Interest rates caplets

The second methodology uses market data on actively traded interest rate caps to form an estimate of a and O. An interest rate cap comprises q caplets, where q is the number of reset dates. Each caplet corresponds to the rate at time and provides payoff at time An interest rate cap provides insurance against adverse upward movements in floating-rate obligations during a future period. An interest rate caplet provides the cap holder with the following payoff ... 

There is still a consistency problem if we want to price interest rate derivatives on zero bonds, like caplets or floorlets, and on swaps, like swaptions, at the same time within one model. The popular market models concentrate either on the valuation of caps and floors or on swaptions, respectively. Musiela and Rutkowski (2005) put it this way We conclude that lognormal market models of forward LIBORs and forward swap rates are inherently inconsistent with each other. A challenging practical question of the choice of a benchmark model for simultaneous pricing and hedging of LIBOR and swap derivatives thus arises. ... 

Note that there is no need for a Caplet 0 covering the very first interest period. As the interest rate for the very first interest period is fixed at the ontset, and is therefore known, there is no need to have an option. Options are only reqnired to provide protection against the unknown. 

The diagram highlights for each caplet the difference between the option period and the protection period. For example, the last caplet has a 4.5 year option period during which interest rates can vary and expose the company to risk. When the caplet expires, the caplet provides compensation over the 6-month protection period if the EURIBOR setting at the outset of that period exceeds the strike rate. 

A ratchet cap is one where the strike price increases when interest rates rise. Unlike a step-up cap, however, this is not according to a preordained schedule. Instead, as each caplet expires, the strike price of all the remaining caplets is reset to the greater of ... 

You can see why a cap is actually a combination of single-period options by thinking about what happens every six months. In our example, the expiry dates of the nine caplets are set to coincide with the company s EURIBOR setting dates. Six months after the loan commences, the rate for the second interest period will be set by reference to the EURIBOR fixing that day. On the same date, the first caplet expires. If EURIBOR is above the strike rate of 3%, the company will exercise the caplet and receive compensation if EURIBOR is lower, the company will simply let the caplet expire worthless. The same process will apply six months later, and so on. 

---