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.