1,924 research outputs found
Modelling skewness in Financial data
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
Extensions of Stein's lemma for the skew-normal distribution
When two random variables have a bivariate normal distribution, Stein's lemma (Stein, 1973, 1981), provides, under certain regularity conditions, an expression for the covariance of the first variable with a function of the second. An extension of the lemma due to Liu (1994) as well as to Stein himself establishes an analogous result for a vector of variables which has a multivariate normal distribution. The extension leads in turn to a generalization of Siegel's (1993) formula for the covariance of an arbitrary element of a multivariate normal vector with its minimum element. This article describes extensions to Stein's lemma for the case when the vector of random variables has a multivariate skew-normal distribution. The corollaries to the main result include an extension to Siegel's formula. This article was motivated originally by the issue of portfolio selection in finance. Under multivariate normality, the implication of Stein's lemma is that all rational investors will select a portfolio which lies on Markowitz's mean-variance efficient frontier. A consequence of the extension to Stein's lemma is that under multivariate skewnormality, rational investors will select a portfolio which lies on a single meanvariance-skewness efficient hyper-surface
On the extended two-parameter generalized skew-normal distribution
We propose a three-parameter skew-normal distribution, obtained by using hidden truncation on a skew-normal random variable. The hidden truncation framework permits direct interpretation of the model parameters. A link is established between the model and the closed skew-normal distribution
Extremal properties of the univariate extended skew-normal distribution
We consider the extremal properties of the highly flexible univariate
extended skew-normal distribution. We derive the well-known Mills' inequalities
and Mills' ratio for the extended skew-normal distribution and establish the
asymptotic extreme-value distribution for the maximum of samples drawn from
this distribution
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