Particle and Kalman Filtering in Finance
Filters infer hidden states (value, volatility, regimes) from noisy price or order-flow observations.
Kalman filters solve linear-Gaussian state-space models exactly with recursive updates.
Particle filters generalise to non-linear or non-Gaussian cases by propagating weighted particles.
In finance, filters track latent volatility, trend, liquidity, or order-flow imbalance in real time.
A latent state (grey) generates noisy observations (red points). The Kalman filter (blue) and a particle filter (green) both try to recover that state in real time. Change noise levels and particle count to see how smoothing and tracking trade off.
With low observation noise, both filters can track the grey state closely. As σ_obs rises, the red dots jump more: the Kalman filter smooths these jumps using its model, while the particle filter uses a cloud of scenarios. Increasing the particle count reduces the green error line: the ensemble is a better approximation of the full Bayesian update.
In finance, the latent state might be trend, volatility, or “efficient price”, and observations are microstructure-noisy quotes. Linear–Gaussian structure favours the Kalman side; non-linear or heavy-tailed effects motivate particle approaches, at the cost of computation.