Abstract
This paper provides an in-depth review about parametric estimation methods for stationary stochastic differential equations (SDEs) driven by Wiener noise with discrete time observations. The short-term interest rate dynamics are commonly described by continuous-time diffusion processes, whose parameters are subject to estimation bias, as data are highly persistent, and discretization bias, as data are discretely sampled despite the continuous-time nature of the model. To assess the role of persistence and the impact of sampling frequency on the estimation, we conducted a simulation study under different settings to compare the performance of the procedures and illustrate the finite sample behavior. To complete the survey, an application of the procedures to real data is provided.
Highlights
Parametric Estimation of DiffusionDiffusion processes described by stochastic differential equations (SDE) are frequently applied in physical, biological and financial fields to model dynamical systems with a disturbance term
Exact maximum likelihood (ML) is available for the Vasicek model, avoiding discretization bias, but biases are homogeneous for all methods, with generalized method of moments (GMM) presenting a slightly higher root mean squared error (RMSE)
We reviewed parametric estimation methods for univariate time-homogeneous SDEs
Summary
Parametric Estimation of DiffusionDiffusion processes described by stochastic differential equations (SDE) are frequently applied in physical, biological and financial fields to model dynamical systems with a disturbance term. New theories of the term structure of interest rate based on pricing models in absence of arbitrage under stochastic environment were emerging: Merton [1] used the interest rate in option pricing modeling it as a stochastic process. Black and Scholes [2] had an important impact on arbitrage models of the term structure of interest rates, as shown in [3,4,5,6,7]. In these models, the interest rate is the solution of the stochastic differential equation, we can use the framework of Markov processes theory for its analytical treatment. The finite sample bias is especially acute when the process is highly persistent, such as time series of interest rates, and alters the valuation of derivatives since short term interest rate models are used to price these instruments [8]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
