Estimation of stochastic volatility with LRD

Understanding the behaviour of market prices is not simple. Stock market prices tend to have complicated distributions with strong skewness and fat tails. One important step in forecasting tomorrow’s price is to estimate the volatility, i.e. how much tomorrow’s price is expected to differ from today’s price. In this paper the volatility is assumed to be a lognormal random process and in addition, it may display long-range dependence (LRD). The aim is to obtain the estimates of the mean, standard deviation and LRD parameter of the volatility process of the S&P 500.