Efficient Implementation of the Heston-Hull & White Model

Abstract

A model with a stochastic interest rate process correlated to a stochastic volatility process is needed to accurately price long-dated contingent claims. Such a model should also price claims efficiently in order to allow for fast calibration. This dissertation explores the approximations for the characteristic function of the Heston-Hull & White model introduced by Grzelak and Oosterlee (2011). Fourier-Cosine expansion pricing is then used to price contingent claims under this model, which is implemented in MATLAB (Fang and Oosterlee, 2008). We find that the model is efficient, accurate and has a relatively simple calibration procedure. In back-tests, it is determined that the Heston-Hull & White model produces better hedging profit and loss results than a Heston (1993) or a Black and Scholes (1973) model.