Analytic Approximations for Valuing Ratchet Caps in the LIBOR Market Model

Abstract

This paper provides two analytic approximation formulas for pricing ratchet caps in the LIBOR market model. The approximate values of a ratchet caplet are represented as sums of Black’s (1976) regular caplet prices. So, these pricing formulas are extremely fast and easily implemented. The formulas can be easily extended to incorporate multiple factors. Illustrative numerical examples are provided and comparisons with results from Monte-Carlo implementation of the LIBOR market model are presented.