论文标题
马尔可夫改装模型的最大似然估计
Maximum Likelihood Estimation for a Markov-Modulated Jump-Diffusion Model
论文作者
论文摘要
我们提出了一种方法，即在数据是扩散过程的离散时间样本时，获得Markov修饰的跳跃 - 扩散模型（MMJDM）的最大似然估计（MLE），跳跃过程遵循拉普拉斯分布，并且扩散的参数由Markov跳跃过程（MJP）控制。数据可以看作是对具有可拖动可能性函数的模型的不完整观察。因此，我们使用EM-Algorithm获得参数的MLE。我们通过模拟数据验证我们的方法。 获得该模型估计的动机是股票价格在不同的时期内具有不同的漂移和波动性。假设这些阶段是由宏观经济环境调节的，这些环境的变化是由不连续性或价格上涨给出的。该模型改善了经典模型的股票价格表示，例如黑色和Scholes或Merton的跳投模型（JDM）。我们将模型符合15年期间亚马逊和Netflix的股票价格，并使用我们的方法估算MLE。
We propose a method for obtaining maximum likelihood estimates (MLEs) of a Markov-Modulated Jump-Diffusion Model (MMJDM) when the data is a discrete time sample of the diffusion process, the jumps follow a Laplace distribution, and the parameters of the diffusion are controlled by a Markov Jump Process (MJP). The data can be viewed as incomplete observation of a model with a tractable likelihood function. Therefore we use the EM-algorithm to obtain MLEs of the parameters. We validate our method with simulated data. The motivation for obtaining estimates of this model is that stock prices have distinct drift and volatility at distinct periods of time. The assumption is that these phases are modulated by macroeconomic environments whose changes are given by discontinuities or jumps in prices. This model improves on the stock prices representation of classical models such as the model of Black and Scholes or Merton's Jump-Diffusion Model (JDM). We fit the model to the stock prices of Amazon and Netflix during a 15-years period and use our method to estimate the MLEs.
