Skewed Libor Market Model and Gaussian HJM explicit approaches to rolled deposit options

Abstract

A simple exotic option (floor on rolled deposit) is studied in the shifted log-normal Libor Market (LMM) and Gaussian HJM models. The shifted log-normal LMM exhibits a controllable volatility skew. An explicit approach is used for both models. Using approximations the price in the LMM is obtained without Monte Carlo simulation. The more precise approximation uses a twisted version of the perdictor-corrector adapted to explicit solutions. The results of the approximation are surprisingly good.Libor Market Model; Heath-Jarrow-Morton; skew; smile; explicit solution; approximation; Bond Market Model; option on composition; existence results