DO INTEREST RATES REALLY FOLLOW CONTINUOUS-TIME MARKOV DIFFUSIONS ?
DO INTEREST RATES REALLY FOLLOW CONTINUOUS-TIME MARKOV DIFFUSIONS ?
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利率真的遵循连续马尔可夫扩散吗？
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
By Yacine Aït
中科院分区：
文献类型：
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作者：
By Yacine Aït
传统上，利率在文献中被建模为连续时间马尔可夫过程，更具体地说是扩散。相比之下，最近的期限结构模型往往意味着非马尔可夫连续时间动态。离散采样的利率数据能否帮助决定哪些连续时间模型是合理的？首先，马尔可夫假设的合理性有多大？将提出对这一假设的检验。第二，如果这个过程是马尔可夫的，它是否可以进一步被确定为扩散，就像大多数理论文献所假设的那样？第二个测试将提出，它测试下保持马尔可夫假设的扩散假设。在马尔可夫世界中，扩散过程的特征在于其样本路径的连续性。很明显，这一条件无法从观察到的样本路径中得到验证：从本质上讲，即使样本路径是连续的，离散采样的利率数据也会表现为一系列离散变化。本文研究离散数据中观察到的不连续性是否是采样的离散性的结果，或者更确切地说，连续时间利率过程的真正的非扩散动力学的证据。这个问题是隔离的数据是一个不完整的离散样本的连续时间扩散的可观察到的影响。本文的答案依赖于测试扩散的条件密度的必要和充分的限制，在所观察到的数据的采样间隔。这一限制刻画了不可观测完全样本路径的连续性，并导出了检验统计量的分布及其一致性和功效性质。我们根据经验发现：（1）短期利率和长期利率都不能单独地被表征为马尔可夫过程;（2）它们共同形成一个马尔可夫系统;（3）收益率曲线的斜率是一个单变量马尔可夫过程;（4）扩散。需要说明的是，这些初步的实证结果对数据集的选择很敏感。
Interest rates have traditionally been modeled in the literature as following continuous-time Markov processes, and more specifically diffusions. By contrast, recent term structure models often imply non-Markovian continuous-time dynamics. Can discretely sampled interest rate data help decide which continuous-time models are sensible? First, how reasonable is the Markovian assumption? A test of this hypothesis will be proposed. Second, if the process is Markovian, can it be identified further as a diffusion, as has been assumed by most of the theoretical literature? A second test will be proposed, which tests the diffusion hypothesis under the maintained Markovian assumption. Within the Markovian world, diffusion processes are characterized by the continuity of their sample paths. It is immediately obvious that this condition cannot be verified from the observed sample path: by nature, even if the sample path were continuous, the discretely sampled interest rate data will appear as a sequence of discrete changes. This paper examines whether the discontinuities observed in the discrete data are the result of the discreteness of sampling, or rather evidence of genuine non-diffusion dynamics of the continuous-time interest rate process. The issue is to isolate the observable implications for the data of being an incomplete discrete sample from a continuous-time diffusion. This paper’s answer relies on testing a necessary and sufficient restriction on the conditional densities of diffusions, at the sampling interval of the observed data. This restriction characterizes the continuity of the unobservable complete sample path. The distribution of the test statistics, as well as their consistency and power properties, are derivted. We find empirically that: (i) neither the short rate nor the long rate can be characterized individually as Markov processes; (ii) jointly, they form a Markovian system; (iii) the slope of the yield curve is a univariate Markov process; (iv) and a diffusion. As a caveat, these preliminary empirical results are sensitive to the choice of dataset.