ABSTRACT
Going beyond modelling the short rate, Heath, Jarrow and Morton developed a model framework for the stochastic evolution of the entire term structure, specified in the form of instantaneous forward rates for all maturities. Under mild technical conditions, it can be shown that all arbitrage free diffusion–based term structure models are special cases of the general Heath/Jarrow/Morton (HJM) framework. This chapter introduces the general HJM setup and considers closed–form and Monte Carlo pricing of contingent claims in the most tractable subset, the multifactor Gauss/Markov HJM term structure models. In order to implement the closed form and Monte Carlo pricing of contingent claims, the multicurrency Gauss/Markov HJM model is represented by a collection of C++ classes. The chapter also discusses the estimation of the exercise boundary for an American put option in the Gauss/Markov HJM model.
