Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices
提出一种在离散观测的连续时间跳跃扩散模型中进行最优滤波的方法，用于估计潜在状态、预测波动率和收益，以及计算似然比等模型诊断，适用于非线性和多变量模型。
This paper provides an optimal filtering methodology in discretely observed continuous-time jump-diffusion models. Although the filtering problem has received little attention, it is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines time-discretization schemes with Monte Carlo methods. It is quite general, applying in nonlinear and multivariate jump-diffusion models and models with nonanalytic observation equations. We provide a detailed analysis of the filter's performance, and analyze four applications: disentangling jumps from stochastic volatility, forecasting volatility, comparing models via likelihood ratios, and filtering using option prices and returns.