Arbitrage-Free Rate Interpolation Scheme for Libor Market Model with Smooth Volatility Term Structure

Abstract

The Libor Market Model describes the evolution of a discrete subset of all interest rates quoted in the market. Generation of the complete yield curve from a simulated set of rates (the so-called "Libor rate interpolation") is one of the basic challenges which are faced by a practical user of LMM. Incorrect implementation can lead to arbitrage in the model and render generated prices invalid. In this paper, we present a rate interpolation scheme which not only is arbitrage-free, but also generates a natural-looking, smooth term structure of interpolated rates' volatilities. It is conceptually simple and computationally efficient.

Keywords: LMM, BGM, rate interpolation, rate, interpolation ,Libor, volatility, volatility term structure

JEL Classification: G13