In this study, we derived analytic expressions for the elliptical truncated moment generating function (MGF), the zeroth, first, and second-order moments of quadratic forms of the multivariate normal, Student's t, and generalised hyperbolic distributions. The resulting formulae were tested in a...

The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle cannot be applied. In this paper, we derive a model-free analytical formula for the implied...

We review the literature about the use of third- and fourth-order moments in finance, the main papers on asset pricing theory with higher-order moments, and the definitions of skewness and kurtosis in the statistical literature. Contagion, skewness and kurtosis investor preferences, and tail...

Countless test statistics can be written as quadratic forms in certain random vectors, or ratios thereof. Consequently, their distribution has received considerable attention in the literature. Except for a few special cases, no closed-form expression for the cdf exists, and one resorts to...