The first systematic analysis of the skew-normal distribution in a scalar case is done by Azzalini (1985). Unlike most of the skewed distributions, the skew-normal distribution allows continuity of the passage from the normal distribution to the skew-normal distribution and is mathematically tractable. The skew-normal distribution and its extensions have been applied in lots of financial applications. This thesis contributes to the recent development of the skew-normal distribution by, firstly, analyzing the the properties of annualization and time-scaling of the skew-normal distribution under heteroskedasticity which, in turn allows us to model financial time series with the skew-normal distribution at different time scales; and, secondly, extending the Skew-Normal-GARCH(1,1) model of Arellano-Valle and Azzalini (2008) to allow for time-varying skewness. Chapter one analyses the performance of the time scaling rules for computing volatility and skewness under the Skew-Normal-GARCH(1,1) model at multiple horizons by simulation and applies the simulation results to the Skew-Normal-Black-Scholes option pricing model introduced by Corns and Satchell (2007). Chapter two tests the Skew-Normal Black-Scholes model empirically. Chapter three extends the Skew-Normal-GARCH(1,1) model to allow for time-varying skewness. The time-varying-skewness adjusted model is then applied to test the relationship between heterogeneous beliefs, shortsale restrictions and market declines.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:614571 |
| Date | January 2014 |
| Creators | Shum, Wai Yan |
| Publisher | University of East Anglia |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://ueaeprints.uea.ac.uk/48762/ |
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