Calibration, Simulation and Hedging in a Heston Libor Market Model with Stochastic Basis

Abstract

We follow Mercurio's extension of the LIBOR market model with stochastic Basis spreads and model the joint evolution of forward rates belonging to the discount curve and corresponding spreads with FRA rates. We consider Heston stochastic-volatility dynamics and show how to calculate the swaption pricing problems in general. We present several different modeling approaches with different stochastic volatility structures and possibilities of correlation. We also describe how to calibrate the models to the swaption matrix with smile. We end the article by giving an overview of how to calculate basis risk deltas and OIS rate deltas of derivative products in this model.

Keywords: LIBOR Market Model, Forwarding Curve, Discount Curve, Swaption Pricing, Calibration, Basis Greeks, Stochastic Volatility, Stochastic Basis, Forward Curves

JEL Classification: E45, G13