The industry standard for pricing an interest rate caplet is Black's formula, which was derived in Section 8.2 from the Libor Market Model. The underlying Libor forward interest rates fL(t, x) are known to be nonlinear, as discussed in Section 6.11.1. A different price of the caplet, namely the linear pricing formula, was derived in Section 9.7 using the bond forward interest rates.

An empirical study is carried out of the linear caplet pricing formula. The main purpose is to ascertain how important are the differences in the Libor Market Model and bond forward interest rates – using the pricing of caps and caplets as an example. In particular, the linear caplet price is compared with the market price of caps and caplets to obtain an estimate of the importance of the nonlinear effects that are the hallmark of the Libor Market Model.

Historical volatility and correlation of forward interest rates are used for predicting the linear caplet price; another approach is to predict the linear price from a parametric formula of the effective volatility using market caplet prices. The study shows that bond forward interest rates generate prices of a caplet and cap with fairly large errors, greater than 17%.

Introduction

The price of a mid-curve caplet has been obtained in Eq. (9.36) based on the bond forward interest rates' model. The result is called the linear caplet price to distinguish it from Black's caplet price, which is an exact result of the Libor Market Model.