Forecasting stock market returns volatility

It has been widely known that the stock market is always volatile and full of risk. How to better capture the volatility and decrease risk accordingly has become a main concern for both investors and researchers. In this thesis, the stochastic volatility model with offset mixture of normal distribution is fitted for financial dataset NASDAQ:LLTC daily stock market returns volatility and one-step-ahead prediction is made based on the AR(1) SV model. Bayesian analysis is fully applied for model fitting and parameter estimation. The Markov Chain Monte Carlo algorithm, using the Metropolis Hasting method, the Forward Filtering Backward Sampling and the Gibbs Sampler is well developed to fit the real data. A small improvement incorporated is the resampling of weights in the discrete normal mixture distribution which is used to approximate a non-normal distribution. Estimated parameters when having weights sampled are compared with the results when weights are fixed. The predictive distribution for one-step-ahead log volatility zT+1 and log transformed stock return yT+1 is given in the graphs. Mean and 95% posterior interval are also provided for both zT+1 and yT +1. FFBS algorithm is first applied to a simulated dataset with normal mixture structure in Dynamic Linear Models. Visual plots with posterior mean and 95% posterior interval are given. Autoregressive model with application of Monte Carlo approximation is also included to model LLTC stock returns.