We consider a stochastic volatility model with Lévy jumps for a log-return process Z=(Zt)t≥0 of the form Z=U+X, where U=(Ut)t≥0 is a classical stochastic volatility process and X=(Xt)t≥0 is an independent Lévy process with absolutely continuous Lévy measure ν. Small-time expansions, of...

Let X=(Xt)t=0 be a Lévy process with absolutely continuous Lévy measure [nu]. Small-time expansions of arbitrary polynomial order in t are obtained for the tails , y0, of the process, assuming smoothness conditions on the Lévy density away from the origin. By imposing additional regularity...

The short-time asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In the present work, novel third-order approximations for close-to-the-money European option prices under an infinite-variation CGMY L\'{e}vy model are derived, and...

This paper gives results related to and including laws of large numbers for (possibly non-harmonizable) periodically and almost periodically correlated processes. These results admit periodically correlated processes that are not continuous in quadratic mean. The idea of a stationarizing random...

Fractional tempered stable motion (fTSm) is defined and studied. FTSm has the same covariance structure as fractional Brownian motion, while having tails heavier than Gaussian ones but lighter than (non-Gaussian) stable ones. Moreover, in short time it is close to fractional stable Lévy motion,...

The short-time asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In the present work, a novel second-order approximation for ATM option prices under the CGMY L\'evy model is derived, and then extended to a model with an...

Converse Poincaré-type inequalities are obtained within the class of smooth convex functions. This is, in particular, applied to the double exponential distribution.

A converse Poincaré-type inequality is obtained within the class of smooth convex functions for the Gaussian distribution.

In the present work, a novel second-order approximation for ATM option prices is derived for a large class of exponential L\'{e}vy models with or without Brownian component. The results hereafter shed new light on the connection between both the volatility of the continuous component and the...

We estimate a median of f(Xt) where f is a Lipschitz function, X is a Lévy process and t is an arbitrary time. This leads to concentration inequalities for f(Xt). In turn, corresponding fluctuation estimates are obtained under assumptions typically satisfied if the process has a regular...