Skew exponential power stochastic volatility model for analysis of skewness, non-normal tails, quantiles and expectiles

This paper proposes a unified framework to analyse the skewness, tail heaviness, quantiles and expectiles of the return distribution based on a stochastic volatility model using a new parametrisation of the skew exponential power (SEP) distribution. The SEP distribution can express a wide range of distribution shapes through two shape parameters and one skewness parameter. Since the asymmetric Laplace and skew normal distributions are included as special cases, the proposed model is related to quantile regression and expectile regression. The efficient and simple Markov chain Monte Carlo estimation methods are also described. The proposed model is demonstrated using the simulated data and real data on daily return of foreign exchange rate.