A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random...

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...

At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for...

The characteristic functions of many affine jump-diffusion models, such as Heston’s stochastic volatility model and all of its extensions, involve multivalued functions such as the complex logarithm. If we restrict the logarithm to its principal branch, as is done in most software packages,...

We consider likelihood inference and state estimation by means of importance sampling for state space models with a nonlinear non-Gaussian observation y ~ p(y|alpha) and a linear Gaussian state alpha ~ p(alpha). The importance density is chosen to be the Laplace approximation of the smoothing...

In this paper we aim to measure actual volatility within a model-based framework using high-frequency data. In the empirical finance literature it is known that tick-by-tick prices are subject to market micro-structure such as bid-ask bounces and trade information. Such market micro-structure...

This discussion paper resulted in an article in the <I>Journal of Empirical Finance</I> (2005). Vol. 12, issue 3, pages 445-475.<p> The increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired...</p></i>