Stochastic volatility models: a maximum likelihood approach
Tareen, Irfan Yousuf
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Volatility is inherent in all empirical financial models. It enters the model through investor behavior with implications to the price of the asset. The specific form this volatility takes is in its dependence on the past values. Financial time series display autocorrelated volatility with the variance of returns on assets changing over time. A method, due to Engle (1982), for modeling volatility is known as autoregressive conditional heteroscedasticity (ARCH). ARCH models securities returns data with a heteroscedastic error term allowing the conditional variance to be a function of the squares of previous observations on stock prices and past variances.|Stochastic Volatility (SVOL) model, an alternative to using the ARCH framework, is examined here that allows both the conditional mean and variance to be driven by separate stochastic processes. The changing variance in such models follows some latent stochastic process. This is an advantage over the ARCH class of models in that the SVOL model has the potential to parsimoniously model the volatility process itself versus an ARCH specification that models the conditional expectation of the volatility. There is evidence in the time-series literature suggesting that correlation between the errors distribution introduces the leverage effect that is important in characterizing the behavior of stock returns. The present analysis tests the hypothesis that the alternate disturbance term assumption would produce improved volatility forecasts in the securities market and ultimately superior timing of entry and exit in the stock/derivative market.|Augmenting the data set and considering correlated error terms results in improved estimates of the standard errors. However, this study, in agreement with some previous analyses, shows a lack of evidence for the leverage effect.