Skewed Libor Market Model and Gaussian HJM Explicit Approaches to Rolled Deposit Options

Abstract

An 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 version of the perdictor-corrector adapted to explicit solutions. The results of the approximation are extremely good.

Keywords: Libor Market Model, Heath-Jarrow-Morton, skew, smile, explicitsolution, approximation, Bond Market Model, option on composition, existence results

JEL Classification: G13, E43, C63