A Monte Carlo Study For The Temporal
Aggregation Problem Using One Factor
Continuous Time Short Rate Models
Author(s)
Y. C. Lin
Abstract
For most continuous time models formulated in finance, there is no closed form
for the likelihood function and estimation of the parameters on the basis of
discrete data will be based on an approximation rather than an exact
discretization. For example, the Euler method introduces discretization bias
because it ignores the internal dynamics that can be excessively erratic. We view
the approximation as a difference equation and note that the solution of the
continuous time model does not satisfy this difference equation. The
effectiveness of the approximation will depend on the rate at which the
underlying process is sampled. We investigate how much it matters: can we get
significantly different estimates of the same structural parameter when we use
say hourly data as compared with using monthly data under given discretization?
If yes, then that discretization when applied to a data set in hand, as is done in
practice, cannot be said to give robust results. We compare numerically the
application of methods by Yu and Phillips (2001), Shoji and Ozaki (1998) and
Ait-Sahalia (2002) in the maximum likelihood estimation of the unrestricted
interest rate model proposed by Chan et al. (1992). We find that reducing the
sampling rate yield large biases in the estimation of the parameters. The Ait-
Sahalia method is shown to offer a good approximation and has the advantage of
reducing some of the temporal aggregation bias.
Keywords: the discretization method.
1 Introduction
The purpose of the paper is to evaluate the performance of different
discretization approximation to a structure continuous time model formulated as
Keywords
the discretization method.
Related Book
Other papers in this volume
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