The purpose of this article is to provide, with the help of a fluctuation identity, a generic link
between a number of known identities for the first passage time and overshoot above/below …

We suggest two new fast and accurate methods, the fast Wiener–Hopf (FWH) method and
the iterative Wiener–Hopf (IWH) method, for pricing barrier options for a wide class of Lévy …

We prove simple general formulas for expectations of functions of a L\'evy process and its
running extremum. Under additional conditions, we derive analytical formulas using the …

We construct a universal Monte Carlo method for pricing the options whose payout function
depends on the final position of the extremum of the Lévy process. The proposed method is …

The pricing problem for American options in Markov-modulated Lévy models is solved. The
early exercise boundaries and prices are calculated using a generalization of Carr's …

We prove simple general formulas for expectations of functions of a random walk and its
running extremum. Under additional conditions, we derive analytical formulas using the …

In this paper, we apply Carr's randomization approximation and the operator form of the
Wiener‐Hopf method to double barrier options in continuous time. Each step in the resulting …

Integral representations for expectations of functions of a stable L\'evy process $ X $ and its
supremum $\bar X $ are derived. As examples, cumulative probability distribution functions …

Motivated by the pricing of first touch digital options in exponential Lévy models and
corresponding credit risk applications, we study numerical methods for solving related …

Pricing and hedging of European, American, barrier options and interest rate derivatives for
wide classes of Lévy driven models is considered in situations where qualitative and …