Extending the G2++ Model: Fitting the Term Structure of Implied Volatility

This paper describes a fast and robust procedure for calibrating a two factor Gaussian model (G2++) with piecewise-constant volatility to a large set of options on interest rates swaps. As far as we know the algorithm implemented is novel as it overcomes some issues affecting highly parameterized models like model identification and the need to employ heuristic optimizations in order to get a good overall fitting. In this sense, our procedure extends the G2++ model ability to reproduce the term structure of volatility implied by interest rate options, similarly to how the Hull and White model extended the Vasicek model in order to perfectly fit the term structure of interest rates.