Maximum likelihood estimation of the Hull–White model

We suggest a maximum likelihood estimation method for the popular Hull–White interest rate model. Our method uses a time series of yield curves to estimate model parameters under both risk-neutral and real-world measures. The suggested approach thus offers a solution to two possible drawbacks of calibration to prices of vanilla interest rate derivatives, the current standard for identification of time-inhomogeneous interest rate models. First, our method allows for derivatives pricing on illiquid markets where prices of vanilla products, which the model is calibrated to, are not available. Second, as we identify the real-world measure, we facilitate the use of the Hull–White model for forecasting and hence risk and portfolio management. The main idea of our approach is to maximise the likelihood of yields in periods subsequent to the time at which the model’s time-dependent parameter is fitted to a market forward rate curve. The empirical part of the paper implements the suggested estimation approach on EUR interest rate data. We investigate in-sample and out-of-sample performance of the estimated model, and compare estimation with calibration to swaption prices.