Diagnostic For Volatility And Local Influence Analysis For The Vasicek Model

Music City Center 

The Ornstein-Uhlenbeck process is widely used in financial engineering to describe the dynamics of interest rates, currency exchange rates, and asset price volatilities. Influential observations may significantly affect the validity of inferential procedures and conclusions drawn from them. Identifying atypical data is, therefore, an essential step in any statistical analysis. The local influence approach is a set of methods designed to detect the effect of small perturbations of the model or data on the inference. In this work, we derive local influence methods for stochastic interest rate models typically used to model and predict interest or exchange rates. In particular, we develop and implement local influence diagnostic techniques based on likelihood displacement. We primarily discuss the Vasicek model with perturbation of the variance and the response. Additionally, we propose a statistic to test the hypothesis of constant volatility based on the Gradient test. 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.

Ornstein-Uhlenbeck processes

Local influence diagnostics

Stochastic interest rate models

Likelihood inference

Gradient test 

Business and Economic Statistics Section