Hidden Markov Models and Sequential Monte Carlo Methods

Replication of Fast Filtering with Large Option Panels

This repository contains a replication project based on the paper:

Arnaud Dufays, Kris Jacobs, Yuguo Liu, Jeroen Rombouts (2022)
Fast Filtering with Large Option Panels: Implications for Asset Pricing
March 24, 2022

The objective is to replicate and compare several filtering and parameter estimation methods for the state-space model considered in the paper, using S&P 500 data, within the framework of the Hidden Markov Models and Sequential Monte Carlo Methods course of the M2DS program.

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Project objectives

The project is structured in successive steps:

1. Bootstrap Particle Filter

2. PMMH (Particle Marginal Metropolis–Hastings)

3. Comparison with Orthogonal MCMC

To simplify the implementation, some parameters may be fixed in intermediate steps in order to reduce the dimensionality of the estimation problem.

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Data

• S&P 500 data, publicly available and easy to obtain online.
• Data sources and preprocessing steps are documented in the repository.
• Large raw datasets are not committed directly; scripts are provided to download and preprocess the data.

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Repository structure

Please refer to Bootstrap_PMMH.ipynb for our implementation of Bootstrap Particle Filter and PMMH (Particle Marginal Metropolis–Hastings).
Please refer to Orthogonal_mcmc_uniform_distribution.ipynb for our implementation of the O-MCMC (Orthogonal particle Markov Chain Monte Carlo) with random parameters.
We also did an implementation of the O-MCMC with parameters near to the ones find in the studied paper in Orthogonal_mcmc_normal_distribution.