We find explicit formulas for the moments of the time integral of an exponential Lévy process. We consider both the cases of unconditional moments and conditional on the Lévy process level at the endpoints of the time interval. We propose a new methodology for reconstructing the unknown...

In this paper we propose a method for pricing Asian options in market models with the risky asset dynamics driven by a Hawkes process with exponential kernel. For these processes the couple (λ(t), X(t)) is affine, this property allows to extend the general methodology introduced by Hubalek,...

In this paper, we consider a novel and efficient method to price equity-linked guaranteed minimumdeath benefits (GMDB) with European-style geometric Asian and arithmetic Asian payoffs. In thesituation of continuous transition of market economy, we assume that the underlying asset price...

A framework for pricing Asian power options is developed when the underlying asset follows a jumpfraction process. The partial differential equation (PDE) in the fractional environment with jump is constructed for such option using general Itô's lemma and self-financing dynamic strategy. With...