When do you need a particle filter instead of a Kalman filter?

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AcadiFi · Accepted Answer

Particle filters (sequential Monte Carlo) approximate the posterior distribution of hidden states by a cloud of weighted samples. Each particle represents one possible state trajectory. At each time step: propagate particles through the transition density, reweight by likelihood of the new observation, and resample to kill unlikely paths. Why this matters at Thornblade: the Heston stochastic volatility model has a nonlinear state transition (v_t = v_{t-1} + kappa(theta - v_{t-1})dt + xi sqrt(v_{t-1}) dW_t). Kalman's linearity assumption fails because volatility of volatility scales with sqrt(v). A particle filter makes no distributional assumptions on the state transition or emission — it only needs to sample from the transition and evaluate the likelihood. ```mermaid flowchart TD A[Initial
Particles] --> B[Propagate
Transition] B --> C[Reweight
Likelihood] C --> D[Resample
High-weight] D --> B ``` A typical setup uses 5,000-20,000 particles for moderate-dimensional latent states. Degeneracy (few particles carrying most weight) is the main practical issue; auxiliary particle filters and systematic resampling mitigate it. Applications: stochastic volatility estimation, regime-switching models with continuous latent factors, term-structure models with nonlinear drift, and default-intensity filtering for credit. AcadiFi Level III candidates rarely see particle filters on the curriculum, but they're essential for any serious buy-side quant role. Combine them with Bayesian parameter learning via particle MCMC for full joint inference.

When do you need a particle filter instead of a Kalman filter?

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