In this paper we study arithmetic Asian options when the underlying stock is driven by
special semimartingale processes. We show that the inherently path dependent problem of …

Fast Fourier transform (FFT) method is now a standard calibration engine. However, in many
situations, such as pricing of deep out-of-the-money European options, FFT produces large …

The story of modelling financial markets with stochastic processes began in 1900 with the
study of Bachelier (1900). He modelled stocks as a Brownian motion with drift. However, the …

We analyze properties of prices of American options under Lévy processes and the related
difficulties for design of accurate and efficient numerical methods for pricing of American …

The purpose of this paper is to introduce a stochastic volatility model for option pricing that
exhibits Lévy jump behavior. For this model, we derive the general formula for a European …

In this article the problem of the American option valuation in a Lévy process setting is
analysed. The perpetual case is first considered. Without possible discontinuities (ie with …

We calculate the leading term of asymptotics of the prices of barrier options and first-touch
digitals near the barrier for wide classes of Lévy processes with exponential jump densities …

In this paper, we discuss the problem of the pricing of American-style options in the
exponential Lévy security market model. This model is typically incomplete, and we derive …

Consider a model of a financial market with a stock driven by a Lévy process and constant
interest rate. A closed formula for prices of perpetual American call options in terms of the …