Poisson limit theorem for the number of excursions above high and medium levels by Gaussian stationary sequences

Asymptotic behavior of the point process of high and medium values of a Gaussian stationary process with discrete time is considered. An approximation by a Poisson cluster point process is given for the point process.Comment: 7 pages, no figure

On asymptotic distribution of maxima of complete and incomplete samples from stationary sequences

AbstractLet (Xn) be a strictly stationary random sequence and Mn=max{X1,…,Xn}. Suppose that some of the random variables X1,X2,… can be observed and denote by M˜n the maximum of observed random variables from the set {X1,…,Xn}. We determine the limiting distribution of random vector (M˜n,Mn) under some condition of weak dependency which is more restrictive than the Leadbetter condition. An example concerning a storage process in discrete time with fractional Brownian motion as input is also given

On maximum of Gaussian non-centered fields indexed on smooth manifolds

The double sum method of evaluation of probabilities of large deviations for Gaussian processes with non-zero expectations is developed. Asymptotic behaviors of the tail of non-centered locally stationary Gaussian fields indexed on smooth manifold are evaluated. In particular, smooth Gaussian fields on smooth manifolds are considered

On double extremes of Gaussian stationary processes

We consider a Gaussian stationary process with Pickands' conditions and evaluate an exact asymptotic behaviorof probability of two high extremes on two disjoint interval

Stochastic Volatility Model with Time-dependent Skew

A formula is derived for the 'effective' skew in a stochastic volatility model with a time-dependent local volatility function. The formula relates the total amount of skew generated by the model over a given time period to the time-dependent slope of the instantaneous local volatility function. A new 'effective' volatility approximation is also derived. The utility of the formulas is demonstrated by building a forward Libor model that can be calibrated to swaption smiles that vary across the swaption grid.Stochastic volatility, volatility smile, time-dependent local volatility, effective volatility, effective skew, average skew, homogenization, averaging principle, effective media, forward Libor model, Libor market model, LMM, BGM, volatility calibration, skew calibration,