Libor Market Model

Abstract

This chapter introduces the LIBOR market model, which is the stan- dard model for derivatives pricing. Because the topic of this book is risk manage- ment, we do not deal with the details of pricing. Instead, this chapter introduces the model, focusing on the implications of the real-world model. First, we give a denition of the LIBOR market model, following Jamshidian (1997). Next, we dene the LIBOR market model under the real-world measure (hereinafter, LMRW), and show, following the method of Yasuoka (2013b), that the model exists. Additionally we nd the models under the spot LIBOR measure and under a forward measure that are implied by the LMRW. Finally, we verify the numerical differences of the LIBOR process according to choice of measure. The study on the real-world model will be developed in Chapter 9.

Keywords: Arbitrage-free, Arbitrage pricing, BGM model, Change of nume- raire, Deterministic volatility, Forward LIBOR, Forward measure, HJM model, LIBOR market model, LIBOR volatility: LMRW, Lognormal distribution, Market price of risk, Martingale approach, Positive interest rate, Real-world measure, Risk-neutral model, Spot LIBOR measure, State price de ator, Ter- minal measure.