Modelling stochastic volatility via factor models: An asymmetric approach
T. Vogel (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Nestor Parolya – Mentor (TU Delft - Statistics)
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Abstract
In this thesis, a factor model which estimates multivariate time series is extended to include an asymmetric relation between the returns of assets and the volatility of said assets. The model proposed in this thesis uses the classical factor model, with univariate logarithmic volatility equations to model the factors as well as the asset innovations. The volatility equations for the factors are extended to contain an asymmetric relationship with the factor returns of the day before. In this thesis, a method to estimate this asymmetric model is developed, the method of estimation mainly relies upon MCMC methods. A method to estimate the logarithmic likelihood for the model is provided as well. This method uses a particle filter to estimate the distribution of the volatility. Using the logarithmic likelihood, it is shown that the asymmetry in the data is identifiable, by comparing the likelihood of the model to the likelihood of the classical factor model, as well as to the likelihood of a factor model with a jump extension. Finally, the model is tested on a real data set of daily returns where its effectiveness is again compared to the classical model and the jump model.