Title: A small sample analysis of discretely observed diffusion processes
Authors: Giuseppina Albano - University of Salerno (Italy) [presenting]
Michele La Rocca - University of Salerno (Italy)
Cira Perna - University of Salerno (Italy)
Abstract: Diffusion processes are commonly used to model stochastic phenomena, such as dynamics of financial securities and short-term loan rates. Several methods for the inference have been proposed, essentially based on MLE or its generalizations. Numerical approximations to the unknown likelihood function also lead to efficient estimators. We consider two well-known processes, Vasicek and CIR models. Sample properties of MLE estimators for the involved parameters of such processes are known when the sample size tends to infinity. Moreover, bootstrap procedures to reduce the bias of the drift estimates can be successfully applied. Other methods also lead to estimators that seem to work well in an asymptotic regime. Anyway, in many applications, data are yearly or quarterly observed, so in the estimation of the involved parameters the asymptotic condition of the sample size means to observe the phenomenon for a long period and likely the time series present structural breaks. This is the case in which Vasicek and CIR models are used in insurance for the valuation of life insurance contracts or also to model short-term interest rates. We focus on small sample properties of some alternative estimators. We consider time series with a length between 10 and 100, typically values observed in these contexts. We perform a simulation study in order to investigate which properties of the parameter estimator still remain valid.