Consistent calibration of HJM models to cap implied volatilities

This article proposes a calibration algorithm that fits multifactor Gaussian models to the implied volatilities of caps with the use of the respective minimal consistent family to infer the forward‐rate curve. The algorithm is applied to three forward‐rate volatility structures and their combination to form two‐factor models. The efficiency of the consistent calibration is evaluated through comparisons with nonconsistent methods. The selection of the number of factors and of the volatility functions is supported by a principal‐component analysis. Models are evaluated in terms of in‐sample and out‐of‐sample data fitting as well as stability of parameter estimates. The results are analyzed mainly by focusing on the capability of fitting the market‐implied volatility curve and, in particular, reproducing its characteristic humped shape. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:1093–1120, 2005