Stochastic Volatility Modelling using Hidden Markov Model

Project carried out for Financial Econometrics class taught by Prof. Christian Brownlees. We estimate a common stochastic volatility model which models the volatility process as a latent state. We infer the dynamics in the time series by utilizing a Hidden Markov Model (HMM) which allows identification by Sequential Monte Carlo.

Code Structure

The following repository contains these scripts:

• run.R - Main pipeline which executes all of the following scripts

• sv_sim.R - Simulates a time series that follows a specified stochastics volatility model

• sir.R - Simulation-based filter (sequential importance sampling)

• csir.R - Simulation-based filter (continuous sequential importance sampling) which is needed for the likelihood estimation

• sv_fit.R - Optimization function for the likelihood

• sv_loglik.R - Compute the likelihood function

• csir.c /csir.so - C version of simulation-based filer for faster performance (default). The R function dyn.load loads the DLL. For few platforms it might require different arguments. If an error shows up, please consult the help page of dyn.load function.

• notebook.ipybn - Notebook showing an example of SV parameters estimation using CSIR.

Dependencies

Required libraries:

• fanplot (tested version 3.4.1; used for heat-map plots)
• nloptr (tested version 1.0.4; used for maximum likelihood estimation)

Instructions

Set as working directory your-directory/StochVol_HMM/code. Execute script run.R (on Linux sudo Rscript run.R); open the notebook file. For faster execution of the maximum likelihood estimation run function sv_fit in mode 2 (estimation without standard errors).