The estimation and filtering for the Stochastic Volatility model

The stochastic volatility model (see Harvey book “Time Series Models”) is commonly used to model the changing variance of stock returns. Whilst the statistical properties of the model are easy to establish, the estimation and filtering are more involved. The exploration of Markov chain Monte Carlo is important, see Shephard and Pitt (97, Biometrika). Additionally, the exploration of different methods for filtering in discrete time, see Pitt and Shephard (JASA, 99) and in continuous time, see Malik and Pitt (JoE, 2011) can be explored.

The marker’s expectation would be as following:

– Originality and independence of the work (note that you are NOT expected to obtain new mathematical results!)
– Mastery and understanding of the topic
– The extent to which the topic is dealt with
– Quality of the dissertation

However, these are just guidelines so take them with a grain of salt.

Mentioning the application of stochastic volatility in financial markets would be helpful.

The stochastic volatility model (see Harvey book “Time Series Models”) is commonly used to model the changing variance of stock returns. Whilst the statistical properties of the model are easy to establish, the estimation and filtering are more involved. The exploration of Markov chain Monte Carlo is important, see Shephard and Pitt (97, Biometrika). Additionally, the exploration of different methods for filtering in discrete time, see Pitt and Shephard (JASA, 99) and in continuous time, see Malik and Pitt (JoE, 2011) can be explored.

One book of reference for this would be Monte Carlo Statistical Methods by C.P.ROBERT and G.Cassela. other references also can be explored.

There is no page limit or requirement but the dissertations are usually between 30 to 40 pages.

All implementations to be done in R or Python.
Implementing methods on Gibbs sampling, Metropolis sampling, Kalman filters and MCMC for financial data would be a good starting point.
I have attached a general Guideline and the code for nonguassian-Gibbs as an example.
please don’t hesitate to ask for more information if needed.