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Likelihood Evaluation of Jump-Diffusion Models Using Deterministic Nonlinear Filters*
Journal of Computational and Graphical Statistics ( IF 2.4 ) Pub Date : 2020-12-11 , DOI: 10.1080/10618600.2020.1840995
Jean-François Bégin 1 , Mathieu Boudreault 2
Affiliation  

In this study, we develop a deterministic nonlinear filtering algorithm based on a high-dimensional version of Kitagawa (1987) to evaluate the likelihood function of models that allow for stochastic volatility and jumps whose arrival intensity is also stochastic. We show numerically that the deterministic filtering method is precise and much faster than the particle filter, in addition to yielding a smooth function over the parameter space. We then find the maximum likelihood estimates of various models that include stochastic volatility, jumps in the returns and variance, and also stochastic jump arrival intensity with the S&P 500 daily returns. During the Great Recession, the jump arrival intensity increases significantly and contributes to the clustering of volatility and negative returns.

中文翻译:

使用确定性非线性滤波器对跳跃扩散模型进行似然评估*

在这项研究中,我们基于 Kitagawa (1987) 的高维版本开发了一种确定性非线性滤波算法,以评估模型的似然函数,这些模型允许随机波动和到达强度也是随机的跳跃。我们从数值上表明,除了在参数空间上产生平滑函数之外,确定性过滤方法比粒子过滤器精确且快得多。然后我们找到各种模型的最大似然估计,包括随机波动率、回报和方差的跳跃,以及标准普尔 500 指数每日回报的随机跳跃到达强度。在大衰退期间,跳跃到达强度显着增加,并导致波动性和负回报的聚集。
更新日期:2020-12-11
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