Diagnostic for Volatility and Local Influence Analysis for the Vasicek Model

The Ornstein–Uhlenbeck process is widely used in modeling biological systems and, in financial engineering, is commonly employed to describe the dynamics of interest rates, currency exchange rates, and asset price volatilities. As in any stochastic model, influential observations, such as outliers, can significantly influence the accuracy of statistical analysis and the conclusions we draw from it. Identifying atypical data is, therefore, an essential step in any statistical analysis. In this work, we explore a set of methods called local influence, which helps us understand how small changes in the data or model can affect an analysis. We focus on deriving local influence methods for models that predict interest or currency exchange rates, specifically the stochastic model called the Vasicek model. We develop and implement local influence diagnostic techniques based on likelihood displacement, assessing the impact of the perturbation of the variance and the response. We also introduce a novel and simple way to test whether the model’s variability stays constant over time based on the Gradient test. The purpose of these methods is to identify potential risks of reaching incorrect conclusions from the model, such as the inaccurate prediction of future interest rates. Finally, we illustrate the methodology using the monthly exchange rate between the US dollar and the Swiss franc over a period exceeding 20 years and assess the performance through a simulation study.