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A Monte Carlo study for the temporal aggregation problem using one factor continuous time short rate models

机译：使用一个因子连续时间短速率模型的蒙特卡罗研究时间聚集问题

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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.
机译：对于在金融制定最连续时间模型，有一个似然函数和离散数据的基础上，参数估计没有封闭的形式将基于近似，而不是一个确切的离散化。例如，欧拉方法引入离散化偏压因为它忽略了内部动力学，可以是过度不稳定。我们认为逼近的差分方程，并注意连续时间模型的解不满足该差分方程。近似的有效性将取决于在该基本过程被采样的速率。我们调查多少重要的：我们可以显著得到相同的结构参数的不同估计，当我们使用说每小时的数据与使用给定的离散下月度数据进行比较？如果是的话，那么，当在实践中应用，以在手的数据集，为完成离散化，不能说给稳定的结果。我们比较数值在Chan等人提出的无限制利率模型的最大似然估计俞和Phillips（2001），商事和尾崎（1998年）和AIT-Sahalia（2002）方法的应用。 （1992）。我们发现，减少了参数估计的采样速率产量大的偏差。将AIT-Sahalia方法被示出为提供一个良好的近似，并具有减少一些时间聚合偏倚的优点。

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