Bayesian inference on volatility in the presence of infinite jump activity and microstructure noise
Bayesian inference on volatility in the presence of infinite jump activity and microstructure noise
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DOI：
10.1214/20-ejs1794
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发表时间：
2019-09
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通讯作者：
Qi Wang;J. E. Figueroa-L'opez;Todd A. Kuffner
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文献类型：
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作者：
Qi Wang;J. E. Figueroa-L'opez;Todd A. Kuffner
基于高频数据的波动率估计是准确计量和控制金融资产风险的关键。一个具有无限跳跃活动和微观结构噪声的L\'{e}vy过程被认为是高频金融数据的最简单但足够准确的模型之一。利用这个模型，我们提出了一个“故意错误指定”后的波动率忽略跳跃组件的过程。错误指定的后验进一步校正的位置偏移和重新缩放的对数似然的简单估计。我们的主要结果建立了Bernstein-von Mises（BvM）定理，该定理指出，建议调整后的后验是渐近高斯的，以一致估计为中心，方差等于Fisher信息的倒数。在不存在微观结构噪声的情况下，我们的方法可以推广到一般Ito半鞅的积分方差的推断.仿真结果证明了所得到的可信区间的准确性，以及基于调整后验的近似贝叶斯推理的频率论性质。
Volatility estimation based on high-frequency data is key to accurately measure and control the risk of financial assets. A L\'{e}vy process with infinite jump activity and microstructure noise is considered one of the simplest, yet accurate enough, models for financial data at high-frequency. Utilizing this model, we propose a "purposely misspecified" posterior of the volatility obtained by ignoring the jump-component of the process. The misspecified posterior is further corrected by a simple estimate of the location shift and re-scaling of the log likelihood. Our main result establishes a Bernstein-von Mises (BvM) theorem, which states that the proposed adjusted posterior is asymptotically Gaussian, centered at a consistent estimator, and with variance equal to the inverse of the Fisher information. In the absence of microstructure noise, our approach can be extended to inferences of the integrated variance of a general It\^o semimartingale. Simulations are provided to demonstrate the accuracy of the resulting credible intervals, and the frequentist properties of the approximate Bayesian inference based on the adjusted posterior.