We present a parallel algorithm and its implementation that computes lower and upper bounds for prices of Bermudan swaptions. The evolving of the underlying forward rates is assumed to follow the extended multi-factor LIBOR market model. We follow the Longstaff-Schwartz least-squares approach in computing a lower bound and the Andersen-Broadie duality-based procedure in computing an upper bound. Parallelisation in the implementation is achieved through POSIX threading. High-performance Intel MKL functions are used for regression and linear algebra operations. The parallel implementation was tested using Bermudan swaptions with different parameters on Intel multi-core machines. In all the tests the parallel program produced close results to those reported in the previous studies. Significant speedups were observed against an efficient sequential implementation built for comparison.