An Accompaniment to a Course on Interest Rate Modeling: With Discussion of Black-76, Vasicek and HJM Models and a Gentle Introduction to the Multivariate LIBOR Market Model

Abstract

The goal of this paper is to help the motivated students with their course on interest rate modeling and/or to help them learn the LIBOR model by themselves. It implies the reader knows what forward rates, caps, and swap[tion]s are and has some knowledge of the quantitative finance: at least Ito Calculus, Black-Scholes-[Merton] Formula, Girsanov’s Theorem (in one dimension is enough) and the risk-neutral pricing. This stuff is usually taught in the first course on continuous financial modeling and is relatively easy. The interest rate modeling is much more complicated. Still those, who carefully read the wonderful Steven Shreve’s book can learn the short-rate models, change of numeraire and Heath-Jarrow-Morton framework. But not the multivariate LIBOR Model (though there is a short section on the one factor LIBOR Model and its relation to the HJM). However, the Bond/IR market is essentially multivariate and the LIBOR Model can be introduced independently. But I could not find any tutorial, which would suit me. So I decided to write my own. It concerns theory only and not the calibration and computational aspects, which are the issues for the future papers.

Keywords: term structure modeling, vasicek model, black formula 76, HLM. multivariate LIBOR Market model, tutorial for self-studying

JEL Classification: A23, C00, E43