Barrier Options on Spot LIBOR Rates under Multi–Factor Gaussian HJM Models

Abstract

Plain vanilla caps and floors already present problems for valuation and risk management because the distributions of forward rates generated by the underlying interest rate process must be evaluated for multiple future dates at the same time. Introducing exotic features like barriers only makes things harder. But using a variety of techniques, including change of numeraire, stochastic time-change, and an approximation to the Radon-Nikodym derivative, Nunes is able to obtain approximate pricing models in closed-form for single-barrier caps and floors in a multivariate Gaussian Heath-Jarrow-Morton framework. Comparisons against a Monte Carlo solution and an alternative quasi-analytic technique demonstrate that this technique can produce a huge improvement in performance, in some cases achieving better accuracy in under a second than Monte Carlo valuation reaches in more than 24 hours.