Exploring Indirect Inference: An application to LIBOR data

For this study, we have chosen a model with γ = 1, identified as BrennanSchwartz in CKLS. We also impose the restrictions α > 0 and β < 0 in order to ensure reversion to the mean [7]. Ideally, we would like to estimate the value of γ as well, but the choice of this model was for simplicity: The maximum likelihood estimates (MLEs) for α, β, and σ can be found explicitly if we assume normally distributed errors. Alternatively, we could have used a model with a fixed value for γ, such as γ = 0.5 (Cox–Ingersoll–Ross) or γ = 1.5 (Variable Rate model). Values of γ greater than 1 were favoured by CKLS [2], whereas the Cox–Ingersall–Ross model with γ = 0.5 was preferred by a robust GMM [4]. There is no broad consensus for the optimal value of γ; therefore, we decided to use the simplest one. Following the standard approach (seen in [2, 7, 4, 3] and others), we discretize the SDE to estimate the parameters: