The purpose of this paper is to derive the stochastic expansion of self-normalized-residual functionals stemming from a class of diffusion type processes observed at high frequency, where total observing period may or may not tend to infinity. The result enables us to construct some explicit...

Let X be a multidimensional diffusion with jumps. We provide sets of conditions under which: X fulfils the ergodic theorem for any initial distribution; and X is exponentially [beta]-mixing. Utilizing the Foster-Lyapunov drift criteria developed by Meyn and Tweedie, we extend several existing...

In a class of continuous-time filtering models with Gaussian limit, we provide a practical scheme of an approximation of a conditional expectation given finite-dimensional observations, in the light of the double Edgeworth expansion. Simple and explicit expressions up to the second order are...

In this paper, we develop a multivariate risk-neutral Lévy process model and discuss its applicabilityin the context of the volatility smile of multiple assets. Our formulation is based upona linear combination of independent univariate Lévy processes and can easily be calibratedto a set of...

The main purpose of this paper is to derive unbiased Monte Carlo estimators of various sensitivity indices for an averaged asset price dynamics governed by the gamma Lévy process. The key idea is to apply a scaling property of the gamma process with respect to the Esscher density transform...

We address the problem of gradient estimation with respect to four characterizing parameters of the Meixner distribution and Lévy process. With the help of the explicit marginal probability density function, the likelihood ratio method is directly applicable, while unbiased estimators may...

Tempered stable processes are widely used in various fields of application as alternatives with finite second moment and long-range Gaussian behaviors to stable processes. Infinite shot noise series representation is the only exact simulation method for the tempered stable process and has...