A Practitioner's Guide to Pricing and Hedging Callable Libor Exotics in Forward Libor Models

Abstract

Callable Libor exotics is a class of single-currency interest-rate contracts that are Bermuda-style exercisable into underlying contracts consisting of fixed-rate, floating-rate and option legs. Bermuda swaptions, callable inverse floaters and callable range accruals are all examples of callable Libor exotics. It is commonly agreed that these instruments are best modeled using forward Libor models. There are many problems, both technical and conceptual, that arise when applying forward Libor models to callable Libor exotics. These problems span calibration, valuation and computation of risk sensitivities. This paper, to the best of our knowledge, is the first comprehensive overview of calibration, pricing and Greeks calculation techniques for callable Libor exotics in forward Libor models. Many technical results and practical methods presented in the paper are original. Others are adaptations, generalizations and extensions of known approaches. Among the technical contributions of this paper are the recommendations for basis functions for the Longstaff-Schwartz valuation algorithm, the extension of the pathwise differentiation method to callable Libor exotics and elegant Greeks formulas that result, novel smoothing techniques for Monte-Carlo, applica- tion of Markovian approximations and PDE methods to the problem of variance reduction, and practical algorithms for obtaining vegas in forward Libor models. In addition, strategies for calibrating forward Libor models for callable Libor exotics are discussed at length.