Barrier Caps and Floors under the LIBOR Market Model with Double Exponential Jumps

The pricing formulas for barrier caps and floors are derived under the framework of the LIBOR market model with double exponential jumps (LMMDJ). The LMMDJ can capture two important empirical features of interest rates: the leptokurtosis and the observed patterns in implied volatilities. The derived pricing formulas are highly efficient and accurate in the pricing of barrier caps and floors compared with Monte Carlo simulation, hence providing useful and efficient pricing formulas for market practitioners.