Modeling asymmetry in volatility response - non-Gaussian innovations approach

Abstract: This thesis is an explorative note on the non-Gaussian innovations of the volatility process. More specifically, the thesis investigates if the decomposition of the Standard Classical Laplace (SCL) distribution to a difference of two exponential is a valid alternative to modelling the asymmetric volatility processes, taking volatility clustering, the leverage effect and asymmetric response in volatility into account. We derive the probability density functions (pdf) and log-likelihood functions for both asymmetric and non-asymmetric case. The pdf exhibit characteristics suitable for modelling the leverage effect, positive kurtosis and fat tails often observed in financial returns, for both the symmetric and asymmetric case. We derive the likelihood function in the non-asymmetric case with regards to the relevant parameters. The likelihood function evaluated concerning past volatility presents a compact solution with the persistence of volatility, whereas, for the other two parameters, the result is complicated. In the asymmetric case, the log-likelihood function is maximized concerning the parameters of interest through simulation. The convergence rate is fast for the AR and lagged volatility parameters, but slower for the asymmetric parameter, which is hard to observe in this setting.