Calibration of the LIBOR market model - implementation in PREMIA*

The calibration of the Brace-Gatarek-Musiela (BGM) and Jamshidian LIBOR interest rate model to the market values of caps and swaptions has proved to involve several numerical stability issues. In this paper we describe a C++ implementation in PREMIA of the stable algorithm for the joint calibration of [7] for the LIBOR market model, from the prices of caps and swaptions. The outline of this paper is as follows. In Section 2 we recall the defi nition of forward rates and contracts, and in Section 3 we present the arbitrage free modeling of zero coupon bonds, cf. [2], [5], [3] for details. In Section 4 we re-derive the BGM model using Itô calculus, cf. [1], [4]. The pricing of caps and swaptions in this model is described in Section 5. Section 6 is devoted to the calibration algorithm of [7].