Abstract
This paper improves the estimation of continuous time stochastic model that treats volatility as a latent variable and compares the forecasting performance of the Kalman filter procedure with Exponential model of Autoregressive Conditional Heteroscedastisity. Our empirical study examines the stock indice TUNINDEX by using the daily close price data over the period December 31, 1997, its creation date, to December 31, 2009. The results suggest the significant existence of leverage effect between TUNINDEX returns and its volatility. Indeed, an unanticipated increase in Tunindex return leads to increased uncertainty that is greater than that induced by an unanticipated drop in return. Thus, the volatility forecasts based on Kalman filter model may outperform those of EGARCH model.
Highlights
One of the main phenomena observed in the process of stock returns is the presence of strong variations over times; these are periods of turbulence in financial markets.Statistically, the existence of these movements results in fat tails in the variations distribution function, calling into question the very strong assumption of Gaussian distribution returns
The results suggest the significant existence of leverage effect between TUNINDEX returns and its volatility
An unanticipated increase in Tunindex return leads to increased uncertainty that is greater than that induced by an unanticipated drop in return
Summary
One of the main phenomena observed in the process of stock returns is the presence of strong variations over times; these are periods of turbulence in financial markets. The existence of these movements results in fat tails in the variations distribution function, calling into question the very strong assumption of Gaussian distribution returns This empirical evidence has led to the invalidation of the famous formula of Black and Scholes (1973) that assumes that returns are generated from a normal distribution whose mean and variance are constant over time. It presents the major inconvenience not to be stationary This type of specification was quickly abandoned for the benefit of the models generating a stationary volatility process, of type mean-reverting. The aim of this paper is to estimate and predict stochastic volatility from these two discretizations approaches above.
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